Question

How do you solve `3- 6v \leq - 21`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(3)` from each side of the inequality to isolate the `v` term while keeping the inequality balanced:

`-color(red)(3) + 3 - 6v <= -color(red)(3) - 21`

`0 - 6v <= -24`

`-6v <= -24`

Now, divide each side of the inequality by `color(blue)(-6)` to solve for `v` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-6v)/color(blue)(-6) color(red)(>=) (-24)/color(blue)(-6)`

`(color(red)(cancel(color(black)(-6)))v)/cancel(color(blue)(-6)) color(red)(>=) 4`

`v color(red)(>=) 4`