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.
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
to both sides so the inequality sign doesn't change.
All possible values of
that are less than or equal to
will satisfy the inequality. Note that
is included in the solution set.
In this case, we can isolate
from both sides of the inequality.
The second inequality is satisfied for all values of
In this case,
included in the solution set.
Comparing Solution Sets
Now we must compare our solution sets. From the first inequality, we know that the solution set consists of all numbers to the left of on the number line, including itself. We will graph the endpoint with a closed circle at
From the second inequality, we know the solution set includes all values to the right of without including Thus, we'll graph the endpoint with an open circle at
The union of these solution sets is all real numbers.
This means that any real number will solve the first, second, or both inequalities.