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522

1x

Example (1) : Solve for x.

multiplying by the lowest common denominator

5222

12

x

10)2(22

12

x

x + 4 = 10

x + 4 – 4 = 10 – 4

x = 6

Part 1: Equations with Fractions

Simplifying Equations Before Solving

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6

7

2

1

3

2x

Example (2) Solve for x.

The lowest common denominator is 6.

6

76

2

1

3

26 x

6

76

2

16

3

26 x 4x + 3 – 3 = 7 – 3

4x = 4

x = 1 6

42

2

6

3

12x

4x + 3 = 7

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3

23

5

2w

Example (3) Solve for w.

2 215 3 15

5 3w

30 3045

5 3w

6w – 45 = 10

6w – 45 + 45 = 10 + 45

19

6w

6 55

6 6

w

6w = 55

The lowest common denominator is 15.

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Example (4) Solve for s.

2(3s + 1) + 5 = 10 expand and simplify first

6s + 2 + 5 = 10

6s + 7 = 10

6s + 7 – 7 = 10 – 7

6s = 3

6 3

6 6

s

1

2s

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Example (5) Solve for k.

3k + 1 + 2k – 4 = 12 simplify first

5 15

5 5

k

5k – 3 = 12

3k + 2k + 1– 4 = 12

5k – 3 + 3 = 12 + 3

5k = 15

k = 3

group like terms

add like terms

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