Question

How do you solve and graph `−44> −2x − 8 ≥ −8`?

Answer 1

See the entire solution process below:

Explanation:

To solve a system of inequalities you need to perform each operation across the entire system to keep the system of inequalities balanced. First, we will add `color(red)(8)` to each segment of the inequality:

`-44 + color(red)(8) > -2x - 8 + color(red)(8) >= -8 + color(red)(8)`

`-36 > -2x - 0 >= 0`

`-36 > -2x >= 0`

Now, we will divide each segment of the system by `color(blue)(-2)` to solve for `x`. However, because we are multiplying or dividing by a negative term we must reverse the inequality signs:

`(-36)/color(blue)(-2) color(red)(<) (-2x)/color(blue)(-2) color(red)(<=) 0/color(blue)(-2)`

`18 color(red)(<) (color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(<=) 0`

`18 < x <= 0`