# How do you solve the equation abs(9x-2)=7?

$x = 1 , - \frac{5}{9}$

#### Explanation:

Consider $\left\mid x \right\mid = 3$. $x$ can be 3 but it can also be $- 3$. And so when evaluating absolute value questions, we need to evaluate positive and negative values.

Positive

$\left\mid 9 x - 2 \right\mid = 7$

$9 x - 2 = 7$

$9 x = 9$

$x = 1$

Negative

$\left\mid 9 x - 2 \right\mid = 7$

$- \left(9 x - 2\right) = 7$

$- 9 x + 2 = 7$

$- 9 x = 5$

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

and we can see this on the graph:

graph{(y-abs(9x-2))(y-0x-7)=0 [-9.58, 10.42, -0.96, 9.04]}