Question

Solve the absolute value equation :| 10n - 8| + 16 = 4

Answer 1

`\boxed{n=-2}`

Solution Steps:

- Steps for solving an absolute value equation-

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1.) Find the absolute value:

• 
  `|10n-8|=10n+8`

- Absolute value just means if there is any negatives then make them positive.

Equation at the end of this step:

• 
  `10n+8+16=4`

2.) Add 8 and 16:

• 
  `8+16=24`

Equation at the end of this step:

• 
  `10n+24=4`

3.) Subtract 24 from both sides:

• 
  `24-24=` Cancels out

• 
  `4-24=-20`

- Since it was adding, you do the opposite, which is why we subtracted.

Equation at the end of this step:

• 
  `10n=-20`

4.) Divide both sides by 10:

• 
  `10n` ÷
  `10=n`

• 
  `-20` ÷
  `10=-2`

- Since it was multiplying, you do the opposite, which is why we divided.

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Answer 2

(10n -8)+16=4 the absolute value equation is 8(-10n-2)+5=101