# How do you solve abs(a-5)/8=5?

Aug 2, 2016

$| a - 5 | = 8 \times 5$

We need to consider two separate situations.

a) The absolute value is positive
b) The absolute value is negative

Starting with the positive case:

$a - 5 = 40$

$a = 45$

Now for the negative case:

$- \left(a - 5\right) = 40$

$- a + 5 = 40$

$- a = 35$

$a = - 35$

Hence, the solution set is $\left\{- 35 , 45\right\}$.

Hopefully this helps!

Aug 2, 2016

$a = 45 \text{ }$ or $\text{ } a = - 35$

#### Explanation:

Absolute value can be negative inside or positive inside. When the value comes out of the absolute value sign it is always positive.

First, multiply both sides by $8$, the opposite of dividing by $8$.

$\frac{a - 5}{8} \times 8 = 5 \times 8$

Since $\frac{8}{8} = 1$, you have

$a - 5 = 40$

$a - 5$ has two possible values. Solve for both values.

$\left(a - 5\right) = + 40 \text{ }$ or $\text{ } a - 5 = - 40$

$a - 5 = + 40 \to$ add $5$ to both sides

$a - \cancel{5} + \cancel{5} = + 40 + 5$

Since $- 5 + 5 = 0$ and $40 + 5 = + 45$, you have

$a = + 45$

$a - 5 = - 40 \to$ add $5$ to both sides

$a - \cancel{5} + \cancel{5} = - 40 + 5$

Once again, $- 5 + 5 = 0$ and $- 40 + 5 = - 35$

$a = - 35$