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Section 3.5. Distributive Property. You must use the Distributive Property first. Then use the rules from Section 3.4 to solve. 3.5 Using the Distributive Property. Key Skills. Solve the equation:. 3( x – 4) = 48. 4( x + 1) = 16. 3 x – 12 = 48. 4 x + 4 = 16.

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Distributive property
Distributive Property

You must use the Distributive Property first.

Then use the rules from Section 3.4 to solve.


Key skills

3.5 Using the Distributive Property

Key Skills

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


Key skills1

3.5 Using the Distributive Property

Key Skills

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


Section 3 5

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


Section 3 5

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?


Section 3 5

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


Section 3 5

-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


Section 3 5

-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


Section 3 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


Assignment
Assignment

Section 3.5

Page 145

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