# How do you solve and graph abs((2p-8)/4)>=9?

Sep 16, 2017

$p \le - 14 \mathmr{and} p \ge 22$

#### Explanation:

Let's consider that:

$| f \left(x\right) | \ge a$ is equivalent to

$f \left(x\right) \le - a \mathmr{and} f \left(x\right) \ge a$

Then

let's solve the equivalent form:

$\frac{2 p - 8}{4} \le - 9 \mathmr{and} \frac{2 p - 8}{4} \ge 9$

Let's multiply all terms by 4 to eliminate fractions:

$2 p - 8 \le - 36 \mathmr{and} 2 p - 8 \ge 36$

let's transfer -8 to the right side and divide all terms by 2:

$2 p \le - 28 \mathmr{and} 2 p \ge 44$

$p \le - 14 \mathmr{and} p \ge 22$