Question

How do you solve `80 - 2w >= 50`?

Answer 1

`w <= 15`

Explanation:

First, subtract `color(red)(80)` from each side of the inequality to isolate the `w` term while keeping the inequality balanced:

`80 - color(red)(80) - 2w >= 50 - color(red)(80)`

`0 - 2w >= -30`

`-2w >= -30`

Now, divide each side of the inequality by `color(blue)(-2)` to solve for `w` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality condition:

`(-2w)/color(blue)(-2) color(red)(<=) (-30)/color(blue)(-2)`

`(color(blue)(cancel(color(black)(-2)))w)/cancel(color(blue)(-2)) color(red)(<=) 15`

`w <= 15`