Question

How do you solve `13x-11<=7x+37`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(11)` and subtract `color(blue)(7x)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`13x - 11 + color(red)(11) - color(blue)(7x) <= 7x + 37 + color(red)(11) - color(blue)(7x)`

`13x - color(blue)(7x) - 11 + color(red)(11) <= 7x - color(blue)(7x) + 37 + color(red)(11)`

`6x - 0 <= 0 + 48`

`6x <= 48`

Now, divide each side of the inequality by `color(red)(6)` to solve for `x` while keeping the inequality balanced:

`(6x)/color(red)(6) <= 48/color(red)(6)`

`(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) <= 8`

`x <= 8`