Question

1. |4n-15|=|n|
2. |2c+8|=|10c|
can you please show the work for both

Answer 1

Problem 1

Answers: n = 3 or n = 5

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Work Shown:

`|4n - 15| = |n|\\\\4n - 15 = n \ \text{ or } \ 4n-15 = -n\\\\-15 = n-4n \ \text{ or } \ -15 = -n-4n\\\\-15 = -3n \ \text{ or } \ -15 = -5n\\\\-3n = -15 \ \text{ or } \ -5n = -15\\\\n = (-15)/(-3) \ \text{ or } \ n = (-15)/(-5)\\\\n = 5 \ \text{ or } \ n = 3\\\\`

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Problem 2

Answers: c = 1 or c = -2/3

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Work Shown:

`|2c+8| = |10c|\\\\2c+8 = 10c \ \text{ or } \ 2c+8 = -10c\\\\8 = 10c-2c \ \text{ or } \ 8 = -10c-2c\\\\8 = 8c \ \text{ or } \ 8 = -12c\\\\8c = 8 \ \text{ or } \ -12c = 8\\\\c = (8)/(8) \ \text{ or } \ c = (8)/(-12)\\\\c = 1 \ \text{ or } \ c = -(2)/(3)`