If we solve each separately, we will find two solution sets. Since the includes the word "or," the union of those sets is the solution to the compound inequality.

### First Inequality

We solve inequalities the same way we would solve equations. We just need to keep in mind that reverses the sign of the inequality. Here, we'll add

$8$ to both sides so the inequality sign doesn't change.

All possible values of

$x$ that are less than or equal to

$12$ will satisfy the inequality. Note that

$12$ is included in the solution set.

### Second Inequality

In this case, we can isolate

$x$ by subtracting

$3$ from both sides of the inequality.

The second inequality is satisfied for all values of

$x$ greater than

$3.$ In this case,

$3$ is

**not** included in the solution set.

### Comparing Solution Sets

Now we must compare our solution sets. From the first inequality, $x≤12,$ we know that the solution set consists of all numbers to the left of $12$ on the number line, including $12$ itself. We will graph the endpoint with a closed circle at $12.$

From the second inequality, $x>3,$ we know the solution set includes all values to the right of $3,$ without including $3.$ Thus, we'll graph the endpoint with an open circle at $3.$

The union of these solution sets is all real numbers.

This means that any real number will solve the first, second, or both inequalities.