© William James Calhoun, 2001

3-3: Solving Multi-Step Equations

OBJECTIVES:You will be able to solve problems by working backwards, and solve equations involving more than one operation.

Working backwards is one problem-solving strategy that can be employed to solve problem.

It can also help with homework problems. If you can not get to the answer from the problem by yourself, you might can work from the answer to the problem to learn how to do similar problems.

EXAMPLE 1: Due to melting, an ice sculpture loses one-half its weight every hour. After 8 hours, it weighs 5/16 of a pound. How much did it weight in the beginning?Work backwards. Now 4hr ago 8hr ago

1hr ago 5hr ago2hr ago 6hr ago3hr ago 7hr ago

5/165/85/45/2 40

20105

80 lbs.Double the weight each hour backward.

© William James Calhoun, 2001

73

2d ( )3 ( )3

35y ( )5 ( )5

3-3: Solving Multi-Step Equations

EXAMPLE 3: Solve each equation.

A. B.

What is on the same side as y?5 and 9

Which is farther from y?9

How is 9 combined with y?added 9

To undo add nine…Subtract 9 from both sides.

What is on the same side as d?2 and 3

Which is farther from y?3

How is 3 combined with y?divided by 3

To undo divide by three…Multiply by 3 on both sides.

Cancel and multiply.

1

1

-9 -9

How are y and 5 combined?divided by 5

To undo divide by 5…Multiply both sides by 5.

Cancel and multiply.

1

1

y = -15

d - 2 = 21

How are d and 2 combined?subtracted 2

To undo subtract 2…Add 2 to both sides.

+2 +2d = 23

695y 7

32d

Write the equation.69

5y

Write the equation.

© William James Calhoun, 2001

3-3: Solving Multi-Step Equations

3b = -51

252

1b3

A quick helpful hint for SOME problems.

You can use it here.You can not use it here.

6114a3

2

1

25

2

1b3

1(3b + 1) = 2(-25)

3b + 1 = -50-1 -1

3 31

1

b = -17

You can cross multiply to solve equations - only when you havefraction = fraction.

© William James Calhoun, 2001

3-3: Solving Multi-Step Equations

EXAMPLE 4: Find three consecutive odd integers whose sum is -15.

Even though we only dealt with consecutive odd integers in our example and practice, the way we set up the problems works for consecutive even integers as well.

If a problem asks for “consecutive integers”, that would be like 2, 3, 4, etc. In that case, the first integer would be “n”, the second “n + 1”, third “n + 2”, etc.

So for consecutive, add one each step. For consecutive odd or even integers, add two each step.

On the consecutive problems, use a chart.

1st

2nd

3rd

n

n + 2

n + 4

Sum means add, so add the numbers down the column.

3n + 6

This must equal -15 from the problem.

3n + 6 = -15 Solve this equation to find the first number.-6 -6

3n = -213 3n = -7

This is the first number. Use the chart to get the other two.

-7

-5

-3

© William James Calhoun, 2001

3-3: Solving Multi-Step Equations

HOMEWORK

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