Question

How do you solve `2x + 24 \leq - 8x - 6`?

Answer 1

See a solution process below:

Explanation:

First, subtract `color(red)(24)` and add `color(blue)(8x)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`color(blue)(8x) + 2x + 24 - color(red)(24) <= color(blue)(8x) - 8x - 6 - color(red)(24)`

`(color(blue)(8) + 2)x + 0 <= 0 - 30`

`10x <= -30`

Now, divide each side of the inequality by `color(red)(10)` to solve for `x` while keeping the inequality balanced:

`10x/color(red)(10) <= -30/color(red)(10)`

`color(red)(cancel(color(black)(10)))x/cancel(color(red)(10)) <= -3`

`x <= -3`