# How do you solve abs(3x - 6)= -5?

Jul 30, 2015

There are no solutions.

#### Explanation:

The absolute value of a number is never negative.

If the problem had been $| 3 x - 6 | = 5$ instead, there would have been two solutions: the unique value of $x$ where $3 x - 6 = 5$ and the unique value of $x$ where $3 x - 6 = - 5$.

$3 x - 6 = 5 \setminus R i g h t a r r o w 3 x = 11 \setminus R i g h t a r r o w x = \frac{11}{3}$

$3 x - 6 = - 5 \setminus R i g h t a r r o w 3 x = 1 \setminus R i g h t a r r o w x = \frac{1}{3}$

So $x = \frac{11}{3}$ and $x = \frac{1}{3}$ are the two solutions of $| 3 x - 6 | = 5$, but that's not how you wrote your original question.