# How do you solve  abs(8-2x)=4?

Oct 16, 2015

$x = 2 \text{ }$ or $\text{ } x = 6$

#### Explanation:

Since you're dealing with the absolute value of an expression, you know that you're going to have to take into account the fact that the absolute value of a real number returns a positive value regardless of the sign of said number.

This implies that you will have two cases, one in which the expression inside the modulus is positive, and the other when it's negative.

• $8 - 2 x \ge 0 \implies | 8 - 2 x | = 8 - 2 x$

The equation takes the form

$8 - 2 x = 4$

$- 2 x = - 4 \implies x = \frac{\left(_ 4\right)}{\left(- 2\right)} = 2$

• $8 - 2 x < 0 \implies | 8 - 2 x | = - \left(8 - 2 x\right)$

This time, you have

$- \left(8 - 2 x\right) = 4$

$- 8 + 2 x = 4$

$2 x = 12 \implies x = \frac{12}{2} = 6$