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

Mar 27, 2017

$x < 8$

#### 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

$3 \left(x - 4\right) < 12$

$x - 4 < 4$

$x < 8$

Equation 2

$4 \left(x + 3\right) < 12$

$x + 3 < 3$

$x < 0$

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.

$\text{ OR }$ 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 $x < 0 \text{ AND } x < 8$, then BOTH conditions have to be true and the solution would be $x < 0$