6th Grade Math Textbook, Fundamentals

 &KDSWHU

14-8

Solve Multistep Equations

Objective To solve multistep linear equations • To solve multistep equations with one variable

on both sides of the equation

On Monday, Parker Library received 10 boxes, each with the

same number of books. Thirteen of the books had been damaged

and were sent back. The next day, 2 more boxes with the same

number of books were delivered. On Wednesday, 3 more boxes

with the same number of books arrived at the library. After the

third delivery, the library had received and kept 137 books.

How many books were in each box of books?

To find the number of books in each box, write and solve

a multistep equation—an equation that involves two or

more operations.

Let xthe number of books in each box.

number of books number of books number of books number of books number of books

in 10 boxes sent back in 2 boxes in 3 boxes delivered and kept

10 x  13  2 x  3 x  137

Solve: 10 x 13  2 x 3 x 137

15 x 13  137

15 x 13  13  137  13

15 x 150 Simplify.

15 x 15  150  15

x 10

So there were 10 books in each box.

Add 13 to

both sides.

Combine

like terms.

Divide both sides by 15.

Check: 10 x 13  2 x  3 x 137

10(10) 13 2(10)3(10) 137

100  13  20  30 137

150 13 137

137  137 Tr u e

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Annie has 20 more DVDs than Kent has. Alvin has 20 times as

many DVDs as Kent has. The total number of Annie’s and Alvin’s

DVDs divided by 5 is 67. Find k, the number of Kent’s DVDs.

Solve:  67

(5)()(67)(5)

k 20  20 k 335 Simplify.

(k 20 k) 20  335 Combine like terms.

21 k 20  20  335  20

21 k 21  315  21 Divide both sides by 21.

k 15

So Kent has 15 DVDs.

k 20  20 k

5

k 20  20 k

5

Subtract 20 from both sides.

Multiply both sides by 5.

Write an equation to

represent the situation.

1

Check:  67

67

67

67  67 Tr u e

335

5

15  20  20 ( 15 )

5

k 20  20 k

5

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