2.4 Solving Multi-Step Equations

Indicators:

PFA7, PFA8, PFA9

Written by ???

Edited by Eddie Judd, Crestwood Middle School

Edited by Dave Wesley, Crestwood Middle School

To Solve: Undo the operations by working backward.

Ex: x + 9 = 6 5

Ask yourself:

• What is the first thing we are doing to x?

• The second thing?

Recall the order of operations as you answer these questions.

• dividing by 5

• adding 9To undo these steps, do

the opposite operations in opposite order.

The DO-UNDO chart

Use a chart as a shortcut to answering the questions.

DO UNDO• ÷5 -9 • +9 ·5

Follow the steps in the ‘undo’ column to isolate the variable.

Ex: x + 9 = 6 5

• First subtract 9. x + 9 - 9 = 6 - 9

5 x = -3

5• Then multiply by 5. (5) x = -3(5)

5 x = -15

Let’s try another!

Complete the do-undo chart.

DO UNDO• -2 ·3 • ÷ 3 +2

To solve for d:• First multiply by 3.• Then add 2.

Ex: d - 2 = 7 3

(3) d - 2 = 7(3) 3 d - 2 = 21 +2 +2 d = 23

Here’s a tricky one!

Remember to always use the sign in front of the number.

DO UNDO• ÷ -7 - 3 • +3 · -7

To solve for a:• First subtract 3. • Then multiply by -7.

Ex: 3 - a = -2 7

• 3 - a = -2 7 -3 -3 - a = -5 7• (-7)(- a) = (-5)(-7) 7 a = 35

Try a few on your own.

• 5z + 16 = 51

• 14n - 8 = 34

• 4b + 8 = 10

-2

Example 1

5z + 16 = 51

Example 2

• 14n - 8 = 34

Example 3

• 4b + 8 = 10

-2

The answers:

DO UNDO• · 5 - 16• +16 ÷ 5

• z = 7

DO UNDO

• · 14 +8

• -8 ÷ 14

• n = 3

DO UNDO• · 4 · -2 • +8 - 8• ÷ -2 ÷ 4 • b = -7

Consecutive Numbers

• Consecutive means-- In order/In sequence.

Ex: 1, 2, 3…

10,11,12…

20, 22, 24, 26… (Evens)

51, 53, 55 etc. . . (Odds)

Let’s try one!!!

Find three consecutive integers that have a sum of 15.

What is this asking?

+ + = 15

Almost there!

+ + = 15• Since we don’t know what the first number

is, let’s call it “n.”

• The next number would be “1 more than n”

• The next would be “2 more than n”

n n + 1 n + 2

Let’s complete the problem!

So the problem looks like this:

n + (n + 1) + (n + 2) = 15 Scary Right?!?

Nah!!!

3n + 3 = 15

LIKE TERMS!!! EASY!!!

Solve It!!

3n + 3 = 15

- 3 - 3

3n = 12___ ___

3 3

n = 4

So if n = 4, (n + 1) = 5 and (n + 2) = 6

Your three consecutive numbers are: 4, 5, and 6

Assignment

Algebra 1• Pg 95 Problems 11-26 all, 29 and 33-37 odds

• Honors Algebra 1• Pg 95 Problems 11-23 odd, 25-28 all, 31-37 all

40-42 all