Question

How do you solve `x+ 8< 3x + 4`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(x)` and `color(blue)(4)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-color(red)(x) + x + 8 - color(blue)(4) < -color(red)(x) + 3x + 4 - color(blue)(4)`

`0 + 4 < -color(red)(1x) + 3x + 0`

`4 < (-color(red)(1) + 3)x`

`4 < 2x`

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

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

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

`2 < x`

Or, we can reverse or "flip" the inequality to state the solution in terms of `x`:

`x > 2`