Question

How do you solve `-2+ 5( 7v - 8) \leq - 217`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(2)` to each side of the inequality to isolate the term in parenthesis while keeping the inequality balanced:

`color(red)(2) - 2 + 5(7v - 8) <= color(red)(2) - 217`

`0 + 5(7v - 8) <= -215`

`5(7v - 8) <= -215`

Next, divide each side of the inequality by `color(red)(5)` to eliminate the need for the parenthesis while keeping the inequality balanced:

`(5(7v - 8))/color(red)(5) <= -215/color(red)(5)`

`(color(red)(cancel(color(black)(5)))(7v - 8))/cancel(color(red)(5)) <= -43`

`7v - 8 <= -43`

Then, add `color(red)(8)` to each side of the inequality to isolate the `v` term while keeping the inequality balanced:

`7v - 8 + color(red)(8) <= -43 + color(red)(8)`

`7v - 0 <= -35`

`7v <= -35`

Now, divide each side of the inequality by `color(red)(7)` to solve for `v` while keeping the inequality balanced:

`(7v)/color(red)(7) <= -35/color(red)(7)`

`(color(red)(cancel(color(black)(7)))v)/cancel(color(red)(7)) <= -5`

`v <= -5`