Question

How do you solve and write the following in interval notation: `-6x + 2< -3x -12`?

Answer 1

See the entire solution process below:

Explanation:

First, add `color(red)(6x)` and `color(blue)(12)` to each side of the inequality to isolate the `x` term while keeping the equation balanced:

`color(red)(6x) - 6x + 2 + color(blue)(12) < color(red)(6x) - 3x - 12 + color(blue)(12)`

`0 + 14 < (color(red)(6) - 3)x - 0`

`14 < 3x`

Now, divide each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`14/color(red)(3) < (3x)/color(red)(3)`

`14/3 < (color(red)(cancel(color(black)(3)))x)/cancel(color(red)(3))`

`14/3 < x`

Or, in interval notation:

`(-oo, 14/3)`