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Section 3.5

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You must use the Distributive Property first.

Then use the rules from Section 3.4 to solve.

3.5 Using the Distributive Property

Solve the equation:

3(x – 4) = 48

4(x + 1) = 16

3x – 12 = 48

4x + 4 = 16

3x – 12+ 12 = 48 + 12

4x + 4– 4 = 16 – 4

3x = 60

4x = 12

3

3

4

4

x = 20

x = 3

3.5 Using the Distributive Property

Solve the equation:

3y – 8 – y = 6

2(x + 5) = –16

2y – 8 = 6

2x + 10 = –16

2y – 8+ 8 = 6 + 8

2x + 10– 10 = –16 – 10

2y = 14

2x = –26

2

2

2

2

y = 7

x = –13

3.5 Using the Distributive Property

Solve the equation:

4x – 8(x + 1) = 8

4t + 7 – t = 19

4x – 8x – 8 = 8

3t + 7 = 19

–4x – 8 = 8

3t + 7– 7 = 19 – 7

–4x – 8 + 8 = 8 + 8

3t = 12

–4x = 16

3

3

–4

–4

t = 4

x = –4

3.5 Using the Distributive Property

Solve the equation, is the answer a solution?

2(x + 4) – 5 = 2x + 3

If all variables cancel, you must look at what’s left.

2x + 8 – 5 = 2x + 3

2x + 3 = 2x + 3

If what’s left is true, answer is all real numbers.

2x + 3 – 2x = 2x + 3 – 2x

3 = 3

If what’s left is not true, answer is no solution.

Does this make sense?

3.5 Using the Distributive Property

Solve the equation, is the answer a solution?

8x – 2(3x – 4) = 5x – 7.

8x + (–6x) + (8) = 5x – 7

2x + 8 = 5x – 7

2x + 8 – 2x = 5x – 7 – 2x

15 = 3x

8 = 3x – 7

3 3

5= x

7 + 8 = 3x – 7 + 7

-10

-10

3.5 Using the Distributive Property

4x – 3(2x + 4) = 8x – 25

4x – 6x – 12 = 8x– 25

–2x – 12 = 8x – 25

–2x = 8x – 25 + 12

–2x = 8x – 13

–2x – 8x = 8x – 13 – 8x

–10x = –13

x = 1.3

-8

-8

3.5 Using the Distributive Property

4x – 7(x + 6) = 5x – 2

4x – 7x – 42 = 5x– 2

–3x – 42 = 5x – 2

–3x = 5x – 2 + 42

–3x = 5x + 40

–3x – 5x = 5x – 5x + 40

–8x = 40

x = –5

8

8

3.5 Using the Distributive Property

5x – 2(3x + 7) = 7x + 12

5x – 6x – 14 = 7x + 12

–x – 14 = 7x + 12

–x – 14 – 12 = 7x + 12 – 12

–x – 26 = 7x

–x + x – 26 = 7x + x

–26 = 8x

–3.25 = x

Section 3.5

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