Question

How do you solve `-12< - 4x + ( - 3)`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(3)` to each side of the inequality to isolate the `x` term while keeping the inequality balanced:

`-12 + color(red)(3) < -4x + (-3) + color(red)(3)`

`-9 < -4x + 0`

`-9 < -4x`

Now, divide each side of the inequality by `color(blue)(-4)` to solve for `x` while keeping the inequality balanced. However, because we are multiplying or dividing an inequality by a negative term we must reverse the inequality:

`(-9)/color(blue)(-4) color(red)(>) (-4x)/color(blue)(-4)`

`9/4 color(red)(>) (color(blue)(cancel(color(black)(-4)))x)/cancel(color(blue)(-4))`

`9/4 color(red)(>) x`

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

`x < 9/4`