Question

How do you solve `6+ 8x < 2( - 3+ 4x )`?

Answer 1

`x in O/`

Explanation:

Your goal here is to isolate `x` on one side of the inequality.

`6 + 8x < 2 * (-3 + 4x)`

Expand the parenthesis to get

`6 + 8x < 2 * (-3) + 2 * 4x`

`6 + 8x < - 6 + 8x`

Now, notice what happens when you subtract `8x` from both sides of the inequality

`6 + color(red)(cancel(color(black)(8x))) - color(red)(cancel(color(black)(8x))) < -6 + color(red)(cancel(color(black)(8x))) - color(red)(cancel(color(black)(8x)))`

`6 < -6`

When is `6` smaller than `-6`?

Never, which implies that this inequality has no real solutions. In other words, regardless of the value of `x` you plug in, the left side of the original inequality will never be smaller than the right side.

`6 + 8x color(red)(cancel(color(black)(<))) 2 * (-3 + 4x), " "(AA) x in RR`

Therefore, you can say that `x in O/`.