3.4 Solving Multistep Equations

3.4 Solving Multistep Equations Objective: Write and solve multistep equations. Standards Addressed: 2.8.8.C: Create and interpret equations that model problem situations. 2.8.8.E: Select and use a strategy to solve an equation.

Ex. 1 Gavin orders office supplies for a small company. Two suppliers offer pens at the same price per box. Supplier A gives a $2 discount on 4 boxes of pens. For the same total cost, Supplier B sells 3 boxes of pens and charges $4 shipping. What is the price of the box of pens?

Ex 2.a. Solve 5x – 6 + -6x + 16. Check the solution. • 5x – 6 = -6x + 16 + 6 + 6 5x = -6x + 22 11x = 22 x = 2 Check x = 2 5(2) – 6 = -6(2) + 16 10 – 6 = -12 + 16 4 = 4

b. Solve 5x -7 = 4x + 3. Check the solution. • 5x – 7 = 4x + 3 + 7 + 7 5x = 4x + 10 x = 10 Check x = 10 5(10) – 7 = 4(10) + 3 50 – 7 = 40+ 3 43 = 43

c. -3m + 12 = 5m + 38. Check the solution. • -3m + 14 = 5m + 38 -3m = 5m + 24 -8m = 24 m = -3 Check x = -3 -3(-3) + 14 = 5 (-3) + 38 9 + 14 = -15 + 38 23 = 23

Ex. 3.a. Solve 5x + 2 = 3x. Check the solution. 5x + 2 = 3x 2 = -2x -1 = x Check x = -1 5(-1) + 2 = 3 (-1) -5 + 2 = -3 -3 = -3

b. Solve 5x – 7 = 4x. Check the solution. 5x – 7 = 4x -7 = -x 7 = x Check x = 7 5(7) -7 = 4 (7) 35 – 7 = 28 28 = 28

c. Solve -3m + 14 = 5m. Check the solution. -3m + 14 = 5m -8m = -14 m = -14/-8 = 7/4

Ex. 4 a.

b. x – 2 = x/5 + 6. • 5x -10 = x + 30 • 5x = x + 40 • 4x = 40 • x = 10

Ex. 5a. Casey is studying for her third test in history. She scored 79 and 88 on her first two tests. What score does Casey need on her third test so that her average will be exactly 85?

b. Cole’s test scores are 87, 86, 91, and 90. What does he need to score on a fifth test to have an average of 90? • 87 + 86 + 91 + 90 + T = 90 5 354 + T = 450 T = 96

3.4 Solving Multistep Equations