Question

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

Answer 1

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

Inequality 1:
`-20<= -6m-2`

`rarr 6m+2 <= 20`

`rarr m<= 3`

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

`rarr 6m+2 >= -58`

`rarr m>= -10`

Synthesis:
`m epsilon [-10,+3]`

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`.