We can use a number line to solve an absolute value inequality. To illustrate the process, we will use the inequality from the exploration:
|x+2|≤3.
To begin, we will focus on |x+2|. This expression asks us to consider the value for which x+2=0. We can see that - 2 makes the equation true. Let's place a temporary point on a number line at - 2.
Now we can consider ≤ 3. We can find the points that are 3 units away from our point at - 2 in both directions. Since the symbol is ≤, we will place closed circles on these points.
Shading the region between will show the solution set to the inequality.
From this number line, we can see that the solution to the inequality is
x ≥ - 5 and x ≤ 1.
