Question

How do you evaluate `(4x - 8) < 4( 6x + 9)`?

Answer 1

See full explanation below

Explanation:

First, you expand all the terms in parenthesis:

`4x - 8 < (color(red)(4) xx 6x) + (color(red)(4) xx 9)`

`4x - 8 < 24x + 36`

Next we subtract the necessary values from both sides of the inequality to isolate the `x` terms on one side of the inequality and the constants on the other side of the inequality while keeping the inequality balanced:

`4x - 8 - color(red)(4x) - color(blue)(36) < 24x + 36 - color(red)(4x) - color(blue)(36)`

`4x - color(red)(4x) - 8 - color(blue)(36) < 24x - color(red)(4x) + 36 - color(blue)(36)`

`0 - 8 - color(blue)(36) < 24x - color(red)(4x) + 0`

`-44 < (24 - 4)x`

`-44 < 20x`

Now we can divide each side of the inequality by `color(red)(20)` to solve for `x` and keep the equation balanced:

`-44/color(red)(20) < (20x)/color(red)(20)`

`-(4 xx 11)/(4 xx 5) < (color(red)(cancel(color(black)(20)))x)/cancel(color(red)(20))`

`-(cancel(4) xx 11)/(cancel(4) xx 5) < x`

`-11/5 < x`

To solve in terms of `x` we can reverse or "flip" the inequality:

`x > -11/5`