Question

How do you solve `5x - 2> 3x + 11`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(2)` and subtract `color(blue)(3x)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(blue)(3x) + 5x - 2 + color(red)(2) > -color(blue)(3x) + 3x + 11 + color(red)(2)`

`(-color(blue)(3) + 5)x - 0 > 0 + 13`

`2x - 0 > 0 + 13`

`2x > 13`

Now, divide each side of the inequality by `color(red)(2)` to solve for `x` while keeping the inequality balanced:

`(2x)/color(red)(2) > 13/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) > 13/2`

`x > 13/2`

Or

`x > 6.5`