Question

How do you solve `4x-7<2x+5`?

Answer 1

See a solution process below:

Explanation:

First, add `color(red)(7)` and subtract `color(blue)(2x)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`4x - color(blue)(2x) - 7 + color(red)(7) < 2x - color(blue)(2x) + 5 + color(red)(7)`

`(4 - color(blue)(2))x - 0 < 0 + 12`

`2x < 12`

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

`(2x)/color(red)(2) < 12/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) < 6`

`x < 6`