warm up solve. 1. x – 3 = 11 2. 18 = x + 4 3. = 42 4. 2x = 52 5. x – 82 = 172 x = 14 course 1...

Warm UpSolve.

1. x – 3 = 11

2. 18 = x + 4

3. = 42

4. 2x = 52

5. x – 82 = 172

x = 14

Course 1

3-9 Solving Decimal Equations

x7

x = 14

x = 294

x = 26

x = 254

Learn to solve equations involving decimals.

Course 1


Course 1


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

Course 1


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

Remember!

Course 1


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.

Course 1


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


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?


6 6

6k = 7.2

Course 1


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


= 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?


· 7

m7

m7

· 7

= 0.6m7

= 0.64.27

?

Course 1


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.

Course 1


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.

Lesson QuizSolve each equation. Check your answer.

1. x – 3.9 = 14.2

2. = 8.3

3. x – 4.9 = 16.2

4. 7x = 47.6

5. The area of the floor in Devon’s room is 35.7 m2.

If the width is 4.2 m, what is the length of the

bedroom?

Insert Lesson Title Here

Course 1


x4

x = 18.1

x = 33.2

x = 21.1

x = 6.8

8.5 m

Course 1

5-10Solving Fraction Equations: Multiplication and Division

Learn to solve equations by multiplying and dividing fractions.

Course 1


Dividing by a number is the same as multiplying by its reciprocal.

Remember!

Course 1

5-10Solving Fraction Equations: Multiplication and DivisionAdditional Example 1A: Solving Equations by

Multiplying and Dividing

Solve each equation. Write the answer in simplest form.

j = 25 35__

j ÷ = 25 ÷ 35__ 3

5__ 3

5__

j • = 25 • 35__ 5

3__ 5

3__

j = 25 • 51 • 3_____

j = 25 • 53__

j = , or 41125

3___ 2

3__

Divide both sides of the equation by .

35__

Multiply by , the reciprocal of .

35__5

3__

Course 1


Additional Example 1B: Solving Equations by Multiplying and Dividing


7x = 25__

7x1__ 2

5__ 1

7__1

7__• = •

x =

2 • 15 • 7____

x =

235__

Multiply both sides by the reciprocal of 7.

The answer is in simplest form.

Course 1


Additional Example 1C: Solving Equations by Multiplying and Dividing


= 65y8__

5y8__ 6

1__ 5

8__5

8__÷ = ÷

y = , or 9 485__

Divide both sides by .

58__

5y8__ 6

1__ 8

5__8

5__• = •

35__

58Multiply by the reciprocal of .

__

Course 1


Check It Out: Example 1A


j = 19 34__

j ÷ = 19 ÷ 34__ 3

4__ 3

4__

j • = 19 • __3

4__ 4

343__

j = 19 • 41 • 3_____

4j = 19 • 3__

76___ 13

j = , or 253

__

Divide both sides of the equation by .

34__

Multiply by , the reciprocal of .

34__4

3__

Course 1


Check It Out: Example 1B


3x = 17__

3x1__ 1

7__ 1

3__1

3__• = •

x =

1 • 17 • 3____

x =

121__

Multiply both sides by the reciprocal of 3.

The answer is in simplest form.

Course 1


Lesson QuizSolve each equation. Write the answer in simplest form.

1. 3x = 2. x = 4

3. x = 14 4. = 9

5. Rebecca used 3 pt of paint to paint of the

trim in her bedroom. How many pints will Rebecca

use for the trim in the entire bedroom?

18__ 1

4__

37__ y

7__

14__

x = 16124__x =

983__ 2

3__x = or 32 y = 63

12

warm up solve. 1. x – 3 = 11 2. 18 = x + 4 3. = 42 4. 2x = 52 5. x – 82 = 172 x = 14 course 1...

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