Question

How do you solve `5 -2x < 7`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(5)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`5 - color(red)(5) - 2x < 7 - color(red)(5)`

`0 - 2x < 2`

`-2x < 2`

Now, divide each side of the inequality by `color(blue)(-2)` 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:

`(-2x)/color(blue)(-2) color(red)(>) 2/color(blue)(-2)`

`(color(blue)(cancel(color(black)(-2)))x)/cancel(color(blue)(-2)) color(red)(>) -1`

`x > -1`