Question

Solve for `x`? `3(x-4)<12 or 4(x+3)<12`

Answer 1

`x<8`

Explanation:

We have two inequalities that are linked with an "or", which means that so long as we have a valid `x` for one of the equations, it'll be part of the solution set (whereas if we had "and", we'd need the `x` values to be valid in both equations).

Let's solve them individually and see what we get:

Equation 1

`3(x-4)<12`

`x-4<4`

`x<8`

Equation 2

`4(x+3)<12`

`x+3<3`

`x<0`

Putting it together

We have `x<8` or `x<0`. Again, so long as we have a valid `x` value in one inequality, it's part of the solution.

`" OR "` means either of the conditions must be true.

`x<8`, since it includes all the solutions in `x<0` and more, is the final answer.

However, if it had been `x<0 " AND " x <8`, then BOTH conditions have to be true and the solution would be `x<0`