# How do you solve and graph abs(1/4x+10)<18?

Jul 14, 2017

$112 < x < 32$ in conjunction with $| \frac{1}{4} x + 10 | < y$

The $112 < x < 32$ limits the domain (input).

#### Explanation:

This is another way of writing:

So we need the condition:

$- 18 < \left(\frac{1}{4} x + 10\right) < 18$

Subtract 10 from everything

$- 28 < \frac{1}{4} x < 8$

Multiply everything by 4

$- 112 < x < 32$

Have a look at the example https://socratic.org/s/aGprwmLH
for the format of presentation $112 < x < 32$

What follows is for your understanding only. The teacher may not be expecting something like it

The shaded area is the feasible region for all $\left(x , y\right)$