# Solve the equation |3x-4|=|3x-5|?

Jan 18, 2017

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

#### Explanation:

As $| 3 x - 4 | = | 3 x - 5 |$, we have

either $3 x - 4 = 3 x - 5$ i.e. $- 4 = - 5$, which is not possible

or $3 x - 4 = - \left(3 x - 5\right)$ i.e. $3 x - 4 = - 3 x + 5$ i.e. $6 x = 9$$3 x - 4 = - \left(3 x - 5\right)$

and $x = \frac{9}{6} = \frac{3}{2}$, which is the only aswer.