Solving Multi-Step Equations

Objective: Solve equations that involve more than one operation.

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

5-Minute Check1. In an intramural basketball game, Annie made 6 points

more than Roberto. Roberto made half as many points as Charlie. Charlie made 3 more points than Darla. If Darla made 9 points, how many points did Annie make?

5-Minute Check1. In an intramural basketball game, Annie made 6 points

more than Roberto. Roberto made half as many points as Charlie. Charlie made 3 more points than Darla. If Darla made 9 points, how many points did Annie make?

12 points

Solving Multi-Step Equations

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

Solving Multi-Step Equations

ExampleSolve b/2 – 8 = 20. Check your solution.

Solving Multi-Step Equations

ExampleSolve b/2 – 8 = 20. Check your solution.

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

Solving Multi-Step Equations

ExampleSolve b/2 – 8 = 20. Check your solution.

b/2 – 8 = 20 b/2 – 8 + 8 = 20 + 8

b/2 = 28

Add 8 to each side.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

ExampleSolve 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.

Solving Multi-Step Equations

Application: Solve the following by first writing an equation.

Teresa’s grocery bill totaled $12.5. If she bought an item for $7.94 and two packs of soft drinks, how much did each pack of soft drinks cost?

Solving Multi-Step Equations

Application: Solve the following by first writing an equation.

Teresa’s grocery bill totaled $12.5. If she bought an item for $7.94 and two packs of soft drinks, how much did each pack of soft drinks cost?

Answer: $2.28

Solving Multi-Step Equations

Assignment: Page 59012 - 32 odd, show your work.