# How do you solve |10x - 28| + 2> 24?

$x > 5 , x < \frac{3}{5}$

#### Explanation:

Let's first isolate the absolute value term:

$\left\mid 10 x - 28 \right\mid + 2 > 24$

$\left\mid 10 x - 28 \right\mid > 22$

With absolute values, we need to evaluate the positive aspect and negative aspect (keep in mind that with, say $\left\mid x \right\mid = 3$, $x$ can be 3 and also can be $- 3$, and so when we evaluate the absolute value, we say $x = \pm 3$. We do the same process for all absolute value questions).

$\pm \left(10 x - 28\right) > 22$

Positive aspect

$10 x - 28 > 22$

$10 x > 50$

$x > 5$

Negative aspect

$- \left(10 x - 28\right) > 22$

$- 10 x + 28 > 22$

$- 10 x > - 6$

we divide by $- 10$ and so we change the direction of the inequality:

$x < \frac{6}{10} = \frac{3}{5}$

Putting it together:

$x > 5 , x < \frac{3}{5}$