Question

How do you solve `-7x + 7 <= - 56`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(7)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-7x + 7 - color(red)(7) <= -56 - color(red)(7)`

`-7x + 0 <= -63`

`-7x <= -63`

Now, divide each side of the inequality by `color(blue)(-7)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative number we must reverse the inequality operator:

`(-7x)/color(blue)(-7) color(red)(>=) (-63)/color(blue)(-7)`

`(color(red)(cancel(color(black)(-7)))x)/cancel(color(blue)(-7)) color(red)(>=) 9`

`x >= 9`