# How do you solve |3x - 5|+ 4= 1?

Apr 28, 2018

No solutions.

#### Explanation:

$| 3 x - 5 | + 4 = 1$

First, we need to make the value in the absolute value by itself. So subtract $4$ from both sides of the equation:
$| 3 x - 5 | = - 3$

Now, we set the value inside the absolute value equal to the other side, and the opposite of the other side.

So we do:
$3 x - 5 = - 3$ AND $3 x - 5 = 3$

$3 x = 2$ $\quad \quad \quad \quad \quad \quad$ AND $\quad \quad \quad \quad 3 x = 8$

$x = \frac{2}{3}$ $\quad \quad \quad \quad \quad \quad$ AND $\quad \quad \quad \quad \quad x = \frac{8}{3}$

$x = \frac{2}{3} ,$ $\frac{8}{3}$

However, we need to check our solutions and see if they really work by plugging them in to the original equation:
$| 3 x - 5 | + 4 = 1$

$| 3 x - 5 | = - 3$

Instead of plugging in the solutions, we can actually see that an absolute value CANNOT equal to a negative number, so the answer is actually no solution.

Hope this helps!