# How do you solve |5x-6|=3?

Dec 27, 2016

$x = \frac{9}{5}$ and $x = \frac{3}{5}$

#### Explanation:

Because this problem contains the absolute value function we need to give it special attention.

The absolute value function transforms a negative or a positive number into a positive number.

Therefore, we need to solve the term inside the absolute value for both the positive and negative value it is equated to, in this case +3 and -3.

Solution 1)

$5 x - 6 = 3$

$5 x - 6 + \textcolor{red}{6} = 3 + \textcolor{red}{6}$

$5 x - 0 = 9$

$5 x = 9$

$\frac{5 x}{\textcolor{b l u e}{5}} = \frac{9}{\textcolor{b l u e}{5}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{b l u e}{5}}} = \frac{9}{\textcolor{b l u e}{5}}$

$x = \frac{9}{5}$

Solution 2)

$5 x - 6 = \textcolor{red}{- 3}$

$5 x - 6 + \textcolor{red}{6} = - 3 + \textcolor{red}{6}$

$5 x - 0 = 3$

$5 x = 3$

$\frac{5 x}{\textcolor{b l u e}{5}} = \frac{3}{\textcolor{b l u e}{5}}$

$\frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{b l u e}{5}}} = \frac{3}{\textcolor{b l u e}{5}}$

$x = \frac{3}{5}$

Dec 27, 2016

$x = \frac{3}{5} \text{ and } x = \frac{9}{5}$ are solutions

#### Explanation:

Given:$\text{ } | 5 x - 6 | = 3$

So in effect we have:

$| \pm 3 | = + 3$

So everything inside the | | must end up as positive or negative 3.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Set } 5 x - 6 = - 3}$

$5 x = + 3$

Divide both sides by 5

$\textcolor{b l u e}{x = + \frac{3}{5}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Set } 5 x - 6 = + 3}$

$5 x = + 9$

Divide both sides by 5

$\textcolor{b l u e}{x = + \frac{9}{5}}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{g r e e n}{\text{Putting it all together}}$

$| 5 x - 6 | = + 3$

$x = \frac{3}{5} \text{ and } x = \frac{9}{5}$ are solutions