Question

How do you solve `-6 ≤ 2 - 3m ≤ 7`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(2)` from each segment of the system of inequalities to isolate the `m` term while keeping the system balanced:

`-6 - color(red)(2) <= 2 - color(red)(2) - 3m <= 7 - color(red)(2)`

`-8 <= 0 - 3m <= 5`

`-8 <= -3m <= 5`

Now, divide each segment by `color(blue)(-3)` to solve for `m` while keeping the system balanced. However, because we are multiplying or dividing inequalities by a negative number we must reverse the inequality operators:

`(-8)/color(blue)(-3) color(red)(>=) (-3m)/color(blue)(-3) color(red)(>=) 5/color(blue)(-3)`

`8/3 color(red)(>=) (color(blue)(cancel(color(black)(-3)))m)/cancel(color(blue)(-3)) color(red)(>=) -5/3`

`8/3 color(red)(>=) m color(red)(>=) -5/3`

Or

`m >= -5/3` and `m <= 8/3`

Or, in interval notation:

`[-5/3, 8/3]`