Question

How do you solve `-30+5x <4(6+8x)`?

Answer 1

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the inequality by multiplying each term within the parenthesis by `color(red)(4)` - the term outside the parenthesis:

`-30 + 5x < color(red)(4)(6 + 8x)`

`-30 + 5x < (color(red)(4) xx 6) + (color(red)(4) xx 8x)`

`-30 + 5x < 24 + 32x`

Next, subtract `color(red)(5x)` and `color(blue)(24)` from each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-30 + 5x - color(red)(5x) - color(blue)(24) < 24 + 32x - color(red)(5x) - color(blue)(24)`

`-30 - color(blue)(24) + 5x - color(red)(5x) < 24 - color(blue)(24) + 32x - color(red)(5x)`

`-54 + 0 < 0 + (32 - 5)x`

`-54 < 27x`

Now, divide each side of the inequality by `color(red)(27)` to solve for `x` while keeping the inequality balanced:

`-54/color(red)(27) < (27x)/color(red)(27)`

`-2 < (color(red)(cancel(color(black)(27)))x)/cancel(color(red)(27))`

`-2 < x`

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

`x > -2`