Example

Solve for $t$: $\quad \displaystyle \left| 3+ \frac{t}{2} \right| > 6$

Solution

Notice that the absolute value expression is already isolated on the left. This inequality tells us that the number between the absolute value bars is more than $6$ units from $0$. In other words,

This compound inequality says that $3+\frac{t}{2}$ is either far to the right on the number line or far to the left. We solve each inequality and the overall solution set of the union.

The first inequality...

The second inequality...

The complete solution set is described by

In interval notation the solution set is

and on the number line it looks like