3-8 Solving Decimal Equations

Learn to solve equations involving decimals.

3-8 Solving Decimal Equations

You can solve equations with decimals using inverse operations just as you solved equations with whole numbers.

$45.20 + m = $69.95–$45.20 –$45.20

m = $24.75

3-8 Solving Decimal Equations

Use inverse operations to get the variable alone on one side of the equation.

Remember!

3-8 Solving Decimal Equations

Additional Example 1A: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

k – 6.2 = 9.5

k – 6.2 = 9.5 6.2 is subtracted from k.

Add 6.2 to both sides to undo the subtraction.

+ 6.2 + 6.2

k = 15.7

Check

k – 6.2 = 9.5Substitute 15.7 for k in the equation.15.7 – 6.2 = 9.5

?

9.5 = 9.5?

15.7 is the solution.

3-8 Solving Decimal Equations

Additional Example 1B: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

6k = 7.2

6k = 7.2

k is multiplied by 6.

Divide both sides by 6 to undo the multiplication.

k = 1.2

Check

6k = 7.2Substitute 1.2 for k in the equation.6(1.2) = 7.2

?

7.2 = 7.2?

1.2 is the solution.

6 6

6k = 7.2

3-8 Solving Decimal Equations

Additional Example 1C: Solving One-Step Equations with Decimals

Solve the equation. Check your answer.

= 0.6

= 0.6

m is divided by 7.

Multiply both sides by 7 to undo the division.

m = 4.2

Check

Substitute 4.2 for m in the equation.

0.6 = 0.6?

4.2 is the solution.

· 7

m7

m7

· 7

= 0.6m7

= 0.64.27

?

3-8 Solving Decimal Equations

Check It Out: Example 1A

Solve the equation. Check your answer.

n – 3.7 = 8.6

n – 3.7 = 8.6 3.7 is subtracted from n.

Add 3.7 to both sides to undo the subtraction.

+ 3.7 + 3.7

n = 12.3

Check

n – 3.7 = 8.6Substitute 12.3 for n in the equation.12.3 – 3.7 = 8.6

?

8.6 = 8.6?

12.3 is the solution.

3-8 Solving Decimal Equations

Check It Out: Example 1B

Solve the equation. Check your answer.

7h = 8.4

7h = 8.4

h is multiplied by 7.

Divide both sides by 7 to undo the multiplication.

h = 1.2

Check

7h = 8.4Substitute 1.2 for h in the equation.7(1.2) = 8.4

?

8.4 = 8.4?

1.2 is the solution.

7 7

7h = 8.4

3-8 Solving Decimal Equations

Check It Out: Example 1C

Solve the equation. Check your answer.

= 0.3

= 0.3

w is divided by 9.

Multiply both sides by 9 to undo the division.

w = 2.7

Check

Substitute 2.7 for w in the equation.

0.3 = 0.3?

2.7 is the solution.

· 9

w9

w9

· 9

= 0.3w9

= 0.32.79

?

3-8 Solving Decimal Equations

The area of a rectangle is its length times its width.

A = lw

Remember!

w

l

3-8 Solving Decimal Equations

Additional Example 2A: Measurement Application

The area of Emily’s floor is 33.75 m2. If its length is 4.5 meters, what is its width?

33.75 = 4.5w

Write the equation for the problem. Let w be the width of the room.

Divide both sides by 4.5 to undo the multiplication.

7.5 = w4.5 4.5

33.75 = 4.5 · w

area = length · width

33.75 = 4.5w

The width of Emily’s floor is 7.5 meters.

3-8 Solving Decimal Equations

Additional Example 2B: Measurement Application

If carpet costs $23 per square meter, what is the total cost to carpet the floor?

Let C be the total cost. Write the equation for the problem.

Multiply.C = 776.25

C = 33.75 · 23

total cost = area · cost of carpet per square meter

The cost of carpeting the floor is $776.25.

3-8 Solving Decimal Equations

Check It Out: Example 2A

The area of Yvonne’s bedroom is 181.25 ft2. If its length is 12.5 feet, what is its width?

181.25 = 12.5w

Write the equation for the problem. Let w be the width of the room.

Divide both sides by 12.5 to undo the multiplication.

14.5 = w12.5 12.5

181.25 = 12.5 · w

area = length · width

181.25 = 12.5w

The width of Yvonne’s bedroom is 14.5 feet.

3-8 Solving Decimal Equations

Check It Out: Example 2B

If carpet costs $4 per square foot, what is the total cost to carpet the bedroom?

Let C be the total cost. Write the equation for the problem.

Multiply.C = 725

C = 181.25 · 4

total cost = area · cost of carpet per square foot

The cost of carpeting the bedroom is $725.