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About Me Graduated from Texas A&M University Born and Raised in San Antonio 6th year teaching at Pearce Teach Algebra II and Pre AP Algebra I Coach Volleyball and Track Grading About the Class Test/ Projects/ After Party = 50% Quizzes = 30% Homework and Participation = 20% Test Given at least a weeks notice Quiz Given at least 3 day notice Homework Graded by completion or partial completion Answers are put on board by students/teacher, gone over as a group Late work will follow Pearce Policy About the Class After Party Take home test 2-4 a Six Weeks Will all accumulate to equal one Test grade Easy way to get a 100 as a Test Grade Projects At least one a Semester First Semester: Linear Project Second Semester: Gym Project, Final Project Mornings Tutoring Monday, Tuesday, Thursdays, and Fridays 8:15am- 8:55am Afterschool Monday or Wednesday with Mr. Tiam 4:10- 5:00 in room B207 Class Online EdLine Class Announcements Class Calendars Power Point Notes Video Lessons Homework Assignments Grades https://portal.risd.org Or you can get there from www.risd.org Supplies Binder/ Folder Pencils Erasers Colored pen/ pencil Grid Paper Spiral Notebook Class gift you pick Box of Tissues Hand Sanitizer Pencils Calculator and Book TI-83 Bring every day Buy your own or borrow one from the school Bring 4 AAA batteries Book One will be issued to you to take home A class set will be available for you to borrow in school Online access through EdLine To Contact Me… Email: [email protected] (Have your parents email by the end of the week) Addition Plus All Together More Than Greater Than Total Sum Increase Subtraction Difference Subtract Less Than Decrease Lost Multiplication Times Per Each Product Multiples Multiply Distribute Division Quotient Per Each Fractions Divide Factors Exponents Squared Raised to Cubed Exponentially To the power of ….. Parenthesis The sum of …… The difference of …… The quotient of …… The product of …… Quantity of ……. VOCABULARY Variable: a letter that represents an unknown value i.e. If 5 = 4x, then x is variable Operation: an action or procedure which produces a new value from one or more input values i.e. addition, subtraction, multiplication, division Constant: a non-varying value; does not change i.e. If 5 = 4x, then 5 and 4 is constant. 5 will always equal 5 Coefficient: A number multiplied by a variable i.e. If 5 = 4x, then 4 is the coefficient VOCABULARY Expression: a mathematical phrase that contains operations, numbers, and/or variables. It does not have an equal sign i.e. 4 + 20 – 7 5(2x+3y) Verbal Expression: a mathematical expression that is represented in using words i.e. Four plus twenty minus seven. Five times the sum of twice a number and three times another number. Numerical Expression: An expression involving only numbers and operations i.e. 4 + 20 – 7 Algebraic Expression: An expression containing at least one variable i.e. 5(2x+3y) VOCABULARY Equation: a mathematical statement that states that two expressions are equivalent. It must have an equal sign. i.e. 34x + 3 = 6x Equation or Expression? 4c 5 6 67 9 4(3 7 a ) 6 9 25 3 Write an algebraic expression for each verbal expression given below. 1) The product of the difference of a number and six, and eight 2) The sum of x and y, multiplied by the quotient of 3 and 4 3) Choose the correct verbal expression for the algebraic expression. 3 x 5 a) the quotient of x squared and 5 b) the quotient of x cubed and 5 c) the product of x squared and 5 d) the product of x cubed and 5 Write a verbal expression for each algebraic expression given below. 4) 5) 1 n4 2 6) 3 x 2 5y 4m 5n Write an algebraic expression or an equation for each verbal expression. 7. The measure of an angle is (5x)° . What is the measure of that angle’s complement? Recall: COMPLEMENTARY ANGLES: Two angles that add up to 90 degrees ANGLES: 8. A square has aSUPPLEMENTARY side length of s. What is it’s perimeter? Two angles that add up to 180 degrees Write an algebraic expression or an equation for each verbal expression. 9. Three plus the quotient of 7 and a number subtracted from two times the same number 10. Write an expression that best represents the amount of money in a bag of quarters, where q is the number of quarters. 11. Lara wants to buy a Rock Band game that is on sale for 35% off the regular price. The regular price of the game is p dollars. Which expression represents the sale price of the game? a) 0.65p b) p 0.35 p c) p 35p d) 0.35p e) 0.35p p Evaluate the following expressions for a 12. Vocabulary 2 bc 4a 3 , b 2.4 , and c 6 . 4 13. 0.5c a a EVALUATE: Recall: to find the value of an ORDER of OPERATIONS: algebraic expression by Parenthesis substituting a number for each variable and simplifying byExponents using the order of operations Multiple Divide Add Subtract Warm Up #1 Write the algebraic expression for each verbal expression. 1. Three less than twice a number. 2n – 3 2. The quotient of 3 and a number subtracted from 8. 8 – (3/x) 3. The sum of a number and five times two. 2(m + 5) VOCABULARY Term: a single number/variable, or the product of several numbers and/or variables separated from another term by a + or - sign in an overall expression. i.e. in 3 + 4x + 5yzw , the 3, 4x, and 5yzw are all terms. Like Terms 4x and 7x Not Like Terms -2x and 9x2 -3a2b3 and 3a2b3 5xy and 7x2y ac and ac 3abc and 3ab If possible, simplify each expression by combining like terms: 1. 4x + x – 3 2. 13x2 + 4 + 10x2 3. 12x2 + 6x4 For all real numbers, a, b and c, a(b + c)=ab + ac, and (b + c)a = ba + ca You multiply a single term over a close set of terms To simplify the expression 2(x + 4), you must distribute the 2 to EVERYTHING inside the parentheses. 2( x + 4) = 2*x + 2*4 =2x+8 Simplify. 4. 8(y + 2x) + 7y Evaluate the expression if x = 1 and y = 4 1 3 Simplify. 5. 6(a – b) – a + 3b Simplify. 1 6. 18 – (2x – 4xy) – (x + y) 2 Write an expression for the following problem, then simplify. 7. The length of a rectangle is 8x – 4 meters long and the width is 4x meters long. 8x – 4 4x a) Write an expression to represent the perimeter of the rectangle in simplest form. b) Evaluate the perimeter if x = 3. Write an expression for the following problem, then simplify. 8. Find the perimeter of the square in terms of r, the radius of the circle. r Write an expression for the following problem, then simplify. 9. Find the perimeter of the image, in simplified form, in terms of x. 2x x2 3 2x 2 5x 1 3x 4 Write an expression for the following problem, then simplify. 10. Two angles are complementary. The larger angle measures 6 more than three times the smaller angle. Write an equation that can be used to find out the measures of both angles, then simplify. Write an expression for the following problem, then simplify. 11. The triangle has angles that measure x°, 3x+10°, and 2(x + 2) °. Write an equation to represent the sum of the angles in the triangle. Recall: ANGLES OF A TRIANGLE: all three angles in any triangle have a sum of 180 degrees Warm Up #2 1 .By hand simplify the following. 1 1 3 1 x x 2 6 4 3 – (1/4)x + (1/2) 2. What is the difference between complementary and supplementary angles? Complementary = 90 degrees Supplementary =180 degrees 3. How many degrees are in triangle? circle? Triangle = 180 degrees Circle = 360 degrees If a = b, then a can be substituted for b in any equation Every time an a appears in an equation or expression, you can replace a with b without changing the value of the expression or equation Let a 2 If 3a 4, then 3 * 2 4 For all real numbers, a, b and c, a(b + c)=ab + ac, and (b + c)a = ba + ca You multiply a single term over a close set of terms To simplify the expression 2(x + 4), you must distribute the 2 to EVERYTHING inside the parentheses. 2( x + 4) = 2x + 8 For all real numbers, a, b and c, if a = b then a+ c =b + c. If two expressions are equal to each other then you can add the same number to both expression without change their equivalence. 3x-5 = 14 3x-5+5=4+5 For all real numbers, a, b and c, if a = b then a – c =b – c. If two expressions are equal to each other then you can subtract the same number to both expression without change their equivalence. 2x+5 = 17 2x+5-5 = 17-5 For all real numbers, a, b and c, if a = b then ac =bc. If two expressions are equal to each other then you can multiply the same number to both expression without change their equivalence. x =12 2 x 2 * =12 * 2 2 For all real numbers, a, b and c, if a = b a b then c c If two expressions are equal to each other then you can divide the same number to both expression without change their equivalence. 3x 15 3x 15 3 3 Name the property that is illustrated in each equation. 1. 14 6t 14 4 14 4. 7t 21 7 7 2. 3. 4 5 x 20 5 5 5. 2(5 x) 2(5) + 2(x) 6. 18x 9 9 36 9 2(5x 12) 23 5x(2) 12(2) 23 Simplify the equation. Justify each step by naming the property being used. 7. Equation: 2(7 3t) 4 Step 1: 14 6t 4 Step 2: 14 6t 14 4 14 Step 3: Step 4: Step 5: 6t 18 6t 18 6 6 t 3 Algebra Tile Legend = x or the variable = -x or the opposite of the variable = 1 unit or a constant = -1 unit or a constant Solve the following equations for the variable given. Show your process using Algebra Tiles and Justify your answer by identify the property you used. 8. x+6 = 2 Solve the following equations for the variable given. Show your process using Algebra Tiles and Justify your answer by identify the property you used. 9. 4x =12 Solve for the Variable. 10. 10 2 x 11. 4.5x 27 VOCABULARY Reciprocal: 1 for a real number a 0 , the reciprocal of is . The product of reciprocals a is 1. i.e. given 5 its reciprocal is Solve for x 5 x 10 9 1 5 Define a variable, write an equation, solve and check your answer. Write you answer in a complete sentence. 13. This year Hays High School had 578 sophomores enrolled. This is 89 less than the number enrolled last year. Write and solve an equation to find the number of sophomores enrolled at Hays High School last year. Define a variable, write an equation, solve and check your answer. Write you answer in a complete sentence. 14. Bob Waters sells boats. He gets to keep one-eighth of his sales as a commission. How much must he sell in order to earn $10,000 in commission? Warm Up #3 1. What operation does the word quotient indicate? Divide 2. What is the coefficient of the term 3xy2? 3 3. Simplify the following: 3(x + 1) – 2(x – 2) 3x+3 – 2x+4 x+7 BOOLEAN ALGEBRA 1 = TRUE 0 = FALSE Solve for the Variable. Use your calculator to check your answer. 1. 6 4 2x 2. 4 7x 3 Solve for the Variable. Use your calculator to check your answer. 3. n 22 7 4. x7 2 4 5. The measures of the angles of a triangle are x , (x 5),(2x 3) . Solve for x and then find the measure of each angle. 6. Ashlyn’s scores on her last 4 Algebra tests were 82, 86, 91 and 96. What does Ashlyn need to make on her fifth test if she needs to make a 90 average? VOCABULARY Consecutive Integers: are integers that follow each other in order. They have a difference of 1 between every two numbers. If n is an integer, then n, n+1, and n+2 will be consecutive integers Even consecutive integers: are even integers that follow each other. They have a difference of 2 between every two numbers. If n is an integer, then 2n, 2n+2, and 2n+4 will be even consecutive integers. Odd consecutive integers Odd consecutive integers are odd integers that follow each other. They have a difference of 2 between every two numbers. If n is an integer, then 2n+1, 2n+3, and 2n+5 will be odd consecutive integers. 7. The sum of two consecutive integers is 47. Find the integers. 8. The sum of two consecutive odd integers is 36. Find the integers. Homework page 96 #2-18 even 48-52 even Warm Up #4 1. What is the Multiplication Property? When you multiply both sides of an equation by the same term. 2. Solve for the variable: m = –16 3. Simplify: 4m 10 2 2 3 1 27 7 5 2 70 Solve for the Variable. 1. 2( x 3) 4 Solve for the Variable. 2. 7 4x (2 x) Solve for the Variable. 3. 2(x 3) 12 5 Solve for the Variable. 4. 1 4 (3n 9) 6n 3 Solve for the Variable. 5. 4n 1 1 3 2 Draw a picture for each, then solve. 6. The length of a rectangle is three times the width. The perimeter is 96 cm, what is the area of the rectangle? Set up an equation, then solve. 7. An angles is 30 degrees more than twice its compliment. Find the measure of both angles. Draw a picture for each, then solve. 8. <A is supplemental to <B . If <A measures 4(4x+5)° and measures <B 2(x+8)°, find the measure of largest angle. Warm Up #5 1. List 2 terms that are alike and 2 terms that are not alike? ~varies~ 2. What is the coefficient of –xyz ? –1 3. Write an equation that is represented for the following algebra tiles. Algebra Tile Legend =x = -x =1 – = -1 2x – 6 = – 3x + 4 Solve the following problems. 1. 4 2n 5 n Solve the following problems. 2. 12h 8 3h 46 Solve the following problems. 3. 6x 4 2 x 6 Solve the following problems. 4. 2( x 3) 5 3( x 1) 5. Solve the following problems. 1 2(n 3) (6n 32) 2 Solve the following problems. 6. You have two consecutive odd numbers. Twice the greater number is 13 less than three times the lesser number. Find the integers. Solve the following problems. 7. A house-painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. a) How long is a job for which both companies will charge the same amount? b) What will that cost be? Warm Up #6 1. What is the difference between 2x² and (2x)² ? (2x)² = 4x² 2. Is the following true or false? True 1 1 1 1 ( ) 2 2 2 2 3. Put the following in order from least to greatest. 1 6 1 2 , , .3, , 3 7 6 9 1 2 1 6 , ,.3, , 6 9 3 7 VOCABULARY All Real Numbers/ Infinite Solutions: When the variables cancel out and there is a true statement. No Solution: When the variables cancel out and there is a false statement Solve the following problems. 1. 3x 8 2( x 4) x 2. Solve the following problems. 1 2 x 3( x 1) 3 x (4 4 x) 2 3. Solve the following problems. 1 1 (14 x 6) 4 (24 x 24) ( x 1) 2 3 4. Solve the following problems. 1 1 (6x 18) (9x 27) 2 3 Warm Up #7 1. What is the difference between infinite solutions, no solutions, and one solutions? Infinite- any number with make the equation true No Solution- there is no real number that will solve the solution One Solution- there is only one answer that can solve the equation. Paper notes/activity Warm Up #8 1. Show two different way to start solving the following equation. 3(x – 1) = 15 3x – 3 = 15 3(x – 1) =15 3 3 Write a let statement and equation for the following situations and then solve as directed. 1. Allison’s cell phone bill for last month was $110. This includes a $60 monthly fee plus the cost of 500 texts. What is the cost of sending one text message that month? Write a let statement and equation for the following situations and then solve as directed. 2. Jessica goes to the State Fair of Texas. The cost of admission is $14.00. The cost for each food coupon is $0.50. a) Write let statements and an equation to represent Jessica’s total cost at the fair. b) If Jessica buys 40 food coupons, how much does she spend total at the Fair? c) If Jessica spends $26.50, how many food coupons did she buy? d)Jessica has $31.00 to spend at the fair, how many food coupons may she buy? Write a let statement and equation for the following situations and then solve as directed. 3. Bulk Up Fitness Club has an enrollment fee of $225 plus $35 per month. a) Write let statements and an equation that represents the total cost c for an individual working out at this fitness club for m months b) What is the cost of a one-year membership? c) WWF contestant, Hulk Man, spent $1030 working out at Bulk Up. How many months did he work out? Write a let statement and equation for the following situations and then solve as directed. 4. Jenna’s PAP Algebra grade after the first 6-weeks was 70%. Jenna wanted to improve her grade, so she began to study at least one extra hour each day. As Jenna tracked the number of extra hours that she studied, she realized her average went up by 2% for every 5 hours of extra study time. a) Write an equation that represents Jenna’s total average as function of h hours. B) What will Jenna’s average be after 300 minutes of extra study time? c) If Jenna’s average is now 86%, how many extra hours did Jenna study? Warm Up #9 Solve for the variable. 1. 3x 1 4 4 x =5 . 2. m 3 7 m = -21 JUST HW Warm Up #10 Solve for the variable. 1. 32 30 2( x 4) X= -5 2. 4 x 2 14 7 x = 21 VOCABULARY Ratio- a comparison of two numbers by division. i.e. a : b a b when b 0 Proportion- states that two ratios are equivalent. i.e. a c b d when b 0, d 0 Cross Products-are equal to each other i.e. a c b d then ad bc Solve the following proportions for the variable. 1. 2. 5 8 2n 3n 24 m 9 m 10 5 11 Solve the following using ratios 3. The ratio of the angles of a triangle is 2:3:4. Find the measure of the largest angle. 4. The length and width of a rectangle are in the ratio 3:2. The perimeter of this rectangle is 73 cm. Find the length and width of the rectangle. VOCABULARY Rate- a ratio of two quantities with different units i.e. 34miles 2 gallons Unit Rate- is when the second quantity is a unit of 1. i.e. 34miles 17miles 2 gallons 1gallons The unit rate is 17 miles per gallon. VOCABULARY Direct Variation - is a linear relationship between two variables, x and y, that can be written in the form , where k is a nonzero constant y kx; k 0 *Proportions are a type of direct variation. *In direct variation as one quantity increases (decreases) so does the other quantity. *In the form y = kx nothing is being added or subtracted to the kx Identify if each of the following is an example of direct variation. If so, identify the constant of variation. 5. y 4x 6. 2x y 10 7. 3x 5y 0 Answer the following questions. 8. Y varies directly with x, and y is 84 when x is 16. a) What is the constant of variation? b) Write a direct variation equation to represent this situation. 9. If y is directly proportional to x and y = 8 when x = 10, what is the value of y when x = 5? Answer the following questions. 10. Look at the table below. If y varies directly with x, what is the constant of variation? 11. The amount of chlorine, c, needed for a swimming pool varies directly with the amount of water, w, needed to fill the pool. If 16 units of chlorine are needed for every 1250 gallons of water, write an equation that represents this situation. Warm Up #11 Set up and solve a proportion for each problem. 1. In Mrs. Willis’s first period Algebra I class, the ratio of boys to girls is 3:4. If there are 28 students in the class, how many girls are there in the class? 3boys:4girls= 7 total x girls = 28 total 16 girls Direct Variation – A Chili Situation Inverse Variation – A Chilly Situation •A Linear Relationship between two variables; x and y • If x increases, then y Increases What is k? •Constant of proportionality •If x decreases, then y decreases • y xy k y x •A Relationship between two variables; x and y • If x increases, then y decreases •If x decreases, then y increases k •y k k xy y x x 1. The number of hours, h, it takes for a block of ice to melt varies inversely as the temperature, t. If it takes 2 hours for a square inch of ice to melt at 65º, find the constant of proportionality, k. 2. Do the tables below demonstrate a relationship of inverse variation? Explain why or why not. Table A Table B Table C x y x y x y 1 30 1 20 2 6 2 15 2 10 3 9 3 10 4 5 6 18 Product Rule of Inverse Variation The product of an x value and it’s corresponding y is equal to the product of any other x and y value in the same situation. x1 y1 x2 y2 x1 y1 3.The number of chairs on a ski lift is inversely proportional to the distance between them. A lift has 70 chairs when they are spaced 24 m apart. If 80 evenly-spaced chairs are used on the lift, how much space will be left between them? 4. Which of the following equations shows a relationship in which y is inversely proportional to x? A B C D E I only II and III only I, II and III II only I and II only 5. The time it takes to fly from LA to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/hr, how long would it take at 800 km/hr? 6. The weight of an object on the moon varies directly as its weight on Earth. With all of his gear on, Neil Armstrong weighted 360 pounds on Earth. When he became the first person to walk on the moon, on July 20, 1969, he weighed 60 pounds in moon weight. If Tara weighs 60 pounds on Earth, how much will she weigh on the moon? 7. The length of a violin string varies inversely as the frequency of its vibrations. A violin string 10 inches long vibrates as a frequency of 512 cycles per second. Find the frequency of an 8 inch long string. 8. In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long? 9. On a balanced seesaw, weight varies inversely as the distance from the fulcrum to the weight. The diagram shows a balanced lever. If the child weighs 80 pounds, approximately how far away from the fulcrum should she sit in order to balance the seesaw? Warm Up #12 Set up and solve a proportion for each problem. 1. What is the formula for direct variation? y = kx 2. What is the formula for inverse variation? y=k x 3. What does k represent? Constant of proportionality Percenta ratio that compares a number to 100 i.e. 25 25% 100 The Percent Proportion- part (is) % whole (of) 100 Set up and use the Percent Proportion to find the missing value. 1. What is 40% of 75? 2. 75% of what number is 33? 3. 30 is what percent of 50? 4. What percent of 200 is 5? VOCABULARY Dimensional Analysis – method for comparing the dimensions in a problem to find relationships between the quantities. Answer the following questions. 5. How many seconds are in a day? 6. You're throwing a pizza party for 15 and figure each person might eat 4 slices. You call up the pizza place and learn that each pizza will cost you $14.78 and will be cut into 12 slices. How much is the pizza going to cost you? homework Page 117 #4-9 all Page 118#20-24 all Page 119 #44-50 even Percent Changeis increase are decrease given as a percent of the original amount. amount of increase or decrease percent change *100% original amount Percent increase- a growth in amount Percent decrease- a reduction in amount Find the percent of change. Is it an increase or decrease? 1. From 25 to 49 2. From 50 to 45 Discount- an amount by which an original price is reduced total original discount Markup- an amount by which a wholesale cost is increased total original markup Commissionis money paid to a person or company for making a sale. total pay base salary commission 3. Admission to a museum is $8. Students receive a 15% discount. How much do students pay for admission? 4. Laura purchased a daily planner for $32. The wholesale cost was $25. What was the percent markup? 5. Jeff receives a 7% commission for selling a house. If his commission was $13,475, what was the selling price of the house? 6. A car salesman earns a 3.5% commission on every car he sells. What is his commission for selling a car for $25,000? 7. A 15% tip is automatically put on the bill at a restaurant when there are more than 6 people in the party. If the eight members of the Bernardo family eat dinner together at the restaurant and their bill totals $156.00 before the tip is added, what will the Bernardo family’s total bill be after the tip? homework Page 135 #2-8 even Page 141 #24-40 even Warm Up #11 Set up and solve a proportion for each problem. 1 2 1. Marlene can walk her dog, Bruno, for miles in 40 minutes. 2 Determine how far she would walk Bruno in one hour. 3.75 miles 2. If Marlene increases her rate to 3 miles in 40 minutes. At this new rate, how far will she walk in 2 hours? 9 miles What is the difference between the two? 5x 10 5x 10 VOCABULARY Equations: • Shows two expression that are equal • Has an equal sign • Have a limited number of solutions • 5x = 10 Inequalities: • Shows some type of relationship between two expressions • Have an inequality sign • Have an unlimited number of solutions • 5x < 10 Graphing Inequalities: If the endpoint IS a solution…. then a closed circle is used to represent that number If the endpoint IS NOT a solution…. then an open circle is used to represent that number Interval Notation: If the endpoint IS a solution…. then a bracket is used to represent that number If the endpoint IS NOT a solution…. then a parenthesis is used to represent that number Sign Less than Graph Internal Notation ( ) Less than and equal to < > ≤ Greater than and equal to ≥ [ ] Greater than ( ) [ ] Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 1. x2 Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 2. x 1 Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 3. 8 x 3 Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 4. 4 3 x Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 5. x 4 2x Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 6. 2x 4 x 3 Graph: Interval Notation: Identify the inequality that goes with each of the following Less than Maximum Greater Than More Than Minimum No more than At most No less than At least Define a variable, write an inequality, and solve each problem. 7. Thirty-six is at least the sum of 20 and a number. Interval Notation: Graph: Define a variable, write an inequality, and solve each problem. 8. The difference of a number and 4 is at most -5. Interval Notation: Graph: Define a variable, write an inequality, and solve each problem. 9.Sami can spend at most $30. She has already spent $14. Write, solve, and graph an inequality to show how much more she can spend. Interval Notation: Graph: Define a variable, write an inequality, and solve each problem. 10. Mrs. Lawrence wants to buy an antique bracelet at an auction. She is willing to bid no more than $550. So far, the highest bid is $475. Write and solve an inequality to determine the amount Mrs. Lawrence can add to the bid. Interval Notation: Graph: Define a variable, write an inequality, and solve each problem. 11. Josh wants to try to break the school bench press record of 282 pounds. He currently can bench press 250 pounds. Write and solve an inequality to determine how many more pounds Josh needs to lift to break the school record. Interval Notation: Graph: HOMEWORK Bookwork Page 177-179 #8-28 even #36-39 all #43-45all Warm Up Write an inequality for each statement. X >0 1. X is a positive number X≥0 2. X is a nonnegative number X<0 3. X is a negative number -∞< x<∞ 4. X is a real number or all real numbers 1.16 Solving MultiStep Inequalities Plug in values for x. 2x 10 2x 10 What do you notice? What is different about the two inequalities? Can you come up with the rule? RULE: When solving for a variable in an inequality and you multiple or divide by a negative, you MUST flip the inequality! Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 1. 2 3x 7 Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation. 2. 2 x 5 5x 4 Graph: Interval Notation: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 3. Interval Notation: 6m (2m 3) 13 Graph: Solve and graph the following inequalities. Then write the solutions to the inequalities in interval notation 4. Graph: 2x 7 9 5 Interval Notation: Define a variable, write an inequality, and solve each problem. 5. Four times a number is less than the sum of two times the same number and six. Find the number. Interval Notation: Graph: Define a variable, write an inequality, and solve each problem. 6. Three more than one-third of a number is no more than nine. Interval Notation: Graph: HOMEWORK Bookwork Page 191-193 #18-26 even #38-48 even #50-54all 1.17 Compound Inequalities Define a variable, write an inequality, and solve each problem. 6. Three more than one-third of a number is no more than nine. Interval Notation: Graph: