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Simplify. 1.) 5(7x – 12) 2.) (–3 – 4p)(3) 3.) 4 - 2(–6y + 2) PE: A1.1.B Solve Problems that can be represented by linear functions, equations, and inequalities. Equivalent: has the same value, “is equal” Inverse Operations: operations that undo each other. Linear Equation: An equation where the variable (or variables) are raised to the first power, do not occur in the denominator, inside a square root, or inside absolute value symbols. Example: 3x-2=27 is a linear equation Are the following Linear Equations? Why? x + 5 = 9 yes x2 + 5 = 9 no -4 + n = 2n - 6 |x + 3| = 7 no yes ( ) distribute • Can you combine like terms on the LHS? ____ (do it!) • Can you combine like terms on the RHS? ____ (do it!) • If variables are on both sides, then make one go away. • What side of the new equation is the variable on? ____ • Is there a number being added or subtracted to THAT side? ___ (get rid of it! Do the opposite.) • Is there a number “next to” the variable? _____ (get rid of it! DIVIDE.) Solve x - 5 = -13 for x. Solve -8 = n - (-4) Simplify. 1.) -5(6x – 11) 2.) (3 – 7p)(-2) 3.) 4 - 2(–7y - 2) Solve x – 7 = 13 for x. Solve 3 – (-x) = 12 for x. Solve using multiplication and division 1.) x 3 2 2.) 3.) 4x = 12 4.) 2 10 m 3 x 30 5 Classify the following numbers as Real, Irrational, Rational, Integers, whole numbers , or natural 1.) 4 2.) ¾ 3.) -2 Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz. Simplify. 1.) 5 4 (3x 4) 6 3 Solve 2.) 2 x5 5 3.) 1 x 6 8 3 The usual rate for taking and projecting professional movies is 24 frames per second. Find the total number of frames in a movie that is 90 minutes long. Simplify: 1.) 5 x 3( x 4) 3.) 7 x 3x 8 5.) 2.) 4.) 6 ( x 3) 5 4 x 3( x 2) Simplify the following: 1.) -6(x+5) 2.) (r-3)(-4) 3.) m(m-1) 4.) (-2a)(a+3) 5.) Write an expression for the perimeter of the trapezoid shown below and simplify it Pg. 148 #1-9, 11-35odd, due 10/21 Extra Credit Pg. 148 # 10-36 even, 57-61 Simplify: 1.) (3x 1) x 2.) 4x 3 23 x 3 Determine whether the given number is a solution to the equation or inequality. 3.) 8+r2 = 16; 4 4.) 2(5y-4)=14; 7.5 5.) Evaluate the following for x=2 1.) 2x+7 2.) 5x2 + 2 3.) 3[(x-2)+x] 4.) 3(x-8)x Determine whether the given number is a solution to the equation or inequality. 5.) 8+r2 = 16; 2 6.) 2(5y-4)=14; 2.2 1.) 2.) 3.) 4.) 5.) 6.) Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz. Equations can have zero, one or many solutions. Equations with one solution can be worked out to equal one number. 7 x 19 2x 55 If the variables cancel out and the numbers left are not equal there are no solutions x2 x4 If the variables cancel out and the two sides of the equal sign are equal then there are many solutions, in fact x would be all real numbers. 3( x 2) 3 x 6 Evaluate the following for x=5 1.) 2x+7 2.) 5x2 + 2 3.) 3[(x-2)+x] 4.) 3(x-8)x Determine whether the given number is a solution to the equation or inequality. 5.) 8+r2 = 16; 5 6.) 2(5y-4)<14; 2 Solve. 7.) 3( x 2) 3x 6 8.) x2 x4 Objective: Solve a formula for one of its variables. The formula for the area of a rectangle is A=lw Find a formula for l in terms of A and w. Rewrite the equation so that x is a function of y 3x y 4 Simplify: 1.) 5 x 3( x 4) 3.) 7 x 3x 8 Solve: 5.) 6 ( x 2 ) 3 x 21 6.) 7 x 19 2x 55 2.) 4.) 6 ( x 3) 5 4 x 3( x 2) 1.) 2.) 3.) 4.) 5.) 6.) Solve using multiplication and division x 3 2 2.) 3.) 4x = 12 4.) 1.) 2 10 m 3 x 30 5 5.) Decide if the following are functions, state the domain and range if they are. Input 1 2 3 4 Output 2 4 5 Input 1 2 3 4 Output 5 7 9 Simplify: 1.) 3.) Solve: 5.) 7 x 19 2x 55 6.) 2.) 5 x 3( x 4) 7 x 3x 8 6( x 2) 3x 21 4.) 6 ( x 3) 5 4 x 3( x 2) A relation is any set of ordered pairs. A Function is a relation where for every input there is exactly one output. f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x f(x) is called function notation. Write y = 3x + 2 in function notation f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x f(x) is called function notation. Write y = 3x + 2 in function notation a.) 7 x 19 2x 55 b.) 6( x 2) 3x 21 a.) 80 9 y 6 y b.) 4(16 3w) 6w a.) 4(1 x) 3x 2( x 1) 1 b.) (12 x 16) 10 3( x 2) 4 Solve: 1.) 17 2x 14 4x 2.) 2(3 x 4) 6 x 9 Quiz When finished with Quiz quietly work on: Pg. 157#1-11, 19-250dd Extra Credit pg. 157 #12-40 even, 47=49 Solve: 1.) 8x 3 5x 18 2.) 4( x 2) 16 Objective: Solve problems using linear equations GAZELLE AND CHEETAH A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second) but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe? A pate of your school yearbook is 8 ½ inches by 11 inches. The left margin is ¾ inch and the space to the right of the pictures is 2 7/8 inches. The space between pictures is 3/16 inch. How wide can each picture be to fit three across the width of the page? Pg. 163 #1-5 Extra Credit pg. 163 #18-21, 27 Solve: 1.) 8x 3 18 2x 2.) 4( x 2) 13 3 x Objective: Solve problems using linear equations Pg. 163 # 6-13 E.C. 14-17, 23-26 Solve: 1.) 7 4m 6m 5 2.) 10(4 y ) 2 y 3.) Round the following numbers to the indicated Place value. a.) 1041, tens place b.) -3.755, hundreds place Objective: Find exact and approximate solutions of equations that contain decimals. Three people want to share equally in the cost of a pizza. The pizza costs $12.89. How much should each person pay? Solve 3.58x-37.40=0.23x=8.32. Round to the nearest hundredth. Pg. 169 #1-13 skip #2 E.C. 14-38 even Solve: 1.) 7.5 4.3m 6.4m 5.1 2.) 4.2 y 2.3 y 3.) Round the following numbers to the indicated Place value. a.) 1041, tens place b.) -3.755, hundredths place A=1/2bh is the formula for the area of a triangle. Solve this formula for b, the base of the triangle. Solve 3x+5 = 20 for x Objective: Rewrite an equation in function form. rewrite the following equations so that y is a function of x 12 x 4 y 16 5 y 15 x 20 Get out your planner and write the following homework assignment in for today: ◦ Pg. 371 #17-28 due Monday Solve: 24a 8 10a 2(4 7a) Pg. 193 #1-21 This is worth a quiz grade