Objective: Solve equations that involve more than one operation.

7-2 Solving Two-Step Equations

5-Minute Check1. Rupesh earned some money mowing lawns one month.

He put half of his money into savings. With the rest, he spent $15 on a new CD, $6 to see a movie, $3 on food, and he still had $24 left. How much money did Rupesh earn mowing lawns that month?

5-Minute Check1. Rupesh earned some money mowing lawns one month.

He put half of his money into savings. With the rest, he spent $15 on a new CD, $6 to see a movie, $3 on food, and he still had $24 left. How much money did Rupesh earn mowing lawns that month?

$96

7-2 Solving Two-Step Equations

To solve two-step equations, first undo operations involving numbers without variables.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8 Add 8 to each side.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28Add 8 to each side.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2

Add 8 to each side.

Multiply each side by 2.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Add 8 to each side.

Multiply each side by 2.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Check: b/2 – 8 = 20

Add 8 to each side.

Multiply each side by 2.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Check: b/2 – 8 = 20 56/2 – 8 ?= 20

Add 8 to each side.

Multiply each side by 2.

Replace b with 56.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Check: b/2 – 8 = 20 56/2 – 8 ?= 20 28 – 8 ?= 20

Add 8 to each side.

Multiply each side by 2.

Replace b with 56.Do the division first.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Check: b/2 – 8 = 20 56/2 – 8 ?= 20 28 – 8 ?= 20

20 ?= 20

Add 8 to each side.

Multiply each side by 2.

Replace b with 56.Do the division first.The solution is 56.

7-2 Solving Two-Step EquationsExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28 2* b/2 = 28 * 2 b = 56

Check: b/2 – 8 = 20 56/2 – 8 ?= 20 28 – 8 ?= 20

20 ?= 20

Add 8 to each side.

Multiply each side by 2.

Replace b with 56.Do the division first.The solution is 56.

SOLVE ON YOUR OWN12b – 7 = 137

COMBINING LIKE TERMS4m + 2m – 7 = 23 combine like terms

first 4m + 2m

6m - 7 = 23 add 7 to both sides + 7 = +7 6m = 30 divide both sides by

6 / 6 / 6 m = 5

COMBINE ON YOUR OWN

7m – 4 + 2m +7 = 30

VARIABLES IN BOTH SIDES5s + 2 = 10 + 1s move all the variables

in one side -1s -1s 4s + 2 = 10 subtract 2 from both

sides - 2 -2 4s = 8 divide both sides by 4 /4 /4 s = 2

SOLVE ON YOUR OWN6b + 9 = 3b + 12