Question

How do you solve `3- 6b \leq - 51`?

Answer 1

See a solution process below:

Explanation:

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

`-color(red)(3) + 3 - 6b <= -color(red)(3) - 51`

`0 - 6b <= -54`

`-6b <= -54`

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

`(-6b)/color(blue)(-6) color(red)(>=) (-54)/color(blue)(-6)`

`(color(blue)(cancel(color(black)(-6)))b)/cancel(color(blue)(-6)) color(red)(>=) 9`

`b >= 9`