Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Line (geometry) wikipedia , lookup
Numerical continuation wikipedia , lookup
Elementary mathematics wikipedia , lookup
System of polynomial equations wikipedia , lookup
Elementary algebra wikipedia , lookup
Recurrence relation wikipedia , lookup
History of algebra wikipedia , lookup
3-3 HW: Pg. 148-152 #10-50eoe,65, & Quiz 1 Pg. 152 #1-11 10.) no 22.) x=-12 14.) yes 26.) x=-3 38.) x=-1 18.) x=12 30.) x=1 1/2 34.) x=15 42.) The left side was simplified incorrectly. Answer should be -1 2/3 46.) x=64 50.) a. If n is an integer, the next two consecutive integers are n+1 and n+2 b. 27, 28, and 29 65.) a. 2/7, 2/7t b. 3/14 t c. 2/7 t + 3/14 t d. 1 represents the entire job, so letting t=time it takes to do the whole job, the fraction of the work Luis can do in that time (2/7 t) plus the fraction for Mei (3/14 t) equals the whole job. Quiz 1 Pg. 152 #1-11 1.) y = 17 2.) x = 4 ½ 3.) z = -2 4.) b = 5/8 5.) q = 32 6.) n = 3 7.) x = -46 8.) y = 12 9.) x = -5 10.) x + 4 = 91. I would have earned 87 points without the bonus points. 11.) 22 2/9 degrees Celsius is the equivalent temperature. Wir2.5 • LESSON 3-4 Solving Equations with Variables On Both Sides Still use the OPPOSITE OPERATION! • Collect the variable terms on the side with the greater variable coefficient • Linear equations do not always have one solution. Some have no solution! • A identity is an equation that is true for all values of the variable. Practice Solve the equation by showing work on BOTH sides if possible. Does the equation have one solution, is it an identity, or does it have no solution? 1.) 2x+3=7x 3.) x-2x+3 3 x 2.) 12-2a=-5a-9 4.) 5x+24 5( x 5) 2 5.) (6c+3)=6(c-3) 3 6.) 6y-(3y-6)=5y-4 Answers : 3 1.) x= ; one solution 2.) a=-7; one solution 5 3.) all real numbers; an identity 4.) no solution 5.) c = 10; one solution 6.) y=5; one solution Practice 2 1.) A video store charges $8 to rent a video game for five days. You must be a member to rent from the store, but the membership fee is free A video game club in town charges only $3 to rent a game for five days, but membership in the club is $50 per year. Which plan is more economical? 2.) You are making pies to sell at a fundraiser. It costs $3 to make each pie, plus a one-time cost of $20 for a pastry blender and a rolling pin. You plan to sell the pies for $5 each. Write an equation to find the number of pies you need to sell to break even. Answers: 1.) x # rented 8x=3x+50 x=10 So if you rent 10 in a year, the cost would be the same, but if you rent more than 10 the club is more economical. Less than 10, the store is more economical. 2.) x = #pies needed to break even 3x+20=5x x = 10 pies So I would need to sell 10 pies to break even. Summary • Is the equation -2(4-x)=2x-8 an identity? Explain why or why not. • Ans: Yes, it is an identity because it is true for all values of x since the left side equals the right side. • Decide if the state is true or false. The solution of x=2x is zero. • Ans: True • Solve 9(9-x)=4x-10. Explain each step along the way. 9 9 9 x 4 x 10 distribute 81 9 x 4 x 10 simplify -4x -4x move the x's on same side 81-13x=-10 simplify -81 move the constants on same side -81 -13 -91 x= -13 -13 x=7 simplify & divide both sides by -13 Check Yourself Pg. 157-159 #12-42e, 56-64 e • #12-42: solve the equation and SHOW WORK on BOTH SIDES • #56-64: mixed review Day 2: Pg. 157 #19-41 odd