# How do you solve the compound inequality -20≤-6m-2≤58 and graph its solution?

Apr 22, 2015

Break up the given compound inequality $- 20 \le - 6 m - 2 \le 58$ into two separate inequalities and treat each separately (before recombining for their intersection).

Inequality 1:
$- 20 \le - 6 m - 2$

$\rightarrow 6 m + 2 \le 20$

$\rightarrow m \le 3$

inequality 2:
-6m-2<= 58#

$\rightarrow 6 m + 2 \ge - 58$

$\rightarrow m \ge - 10$

Synthesis:
$m \epsilon \left[- 10 , + 3\right]$

Graph Solution:
This is somewhat more problematic since we don't really have an equation to graph. I suppose you could draw a number line and indicate the range along it...

or identify $m$ with values along the Y-axis and draw a band of values showing that those values apply for all values of $x$.