Absolute Value Inequalities
Now let’s look at how absolute values work in inequalities. Consider the inequality |x| < 3. Numbers like 1, 2, 1.5, and 2.9 would work, but numbers like –1, -2, -1.5, and –2.9 would also work, since their magnitude is also less than three. We can also think of this problem as asking what numbers are within 3 units of zero on the number line. This is going to extend both left and right from zero.
From this, we can conclude that |x| < 3 can be rewritten as { x | - 3 < x < 3} , since x is less than three, but if it were smaller than –3, the magnitude would no longer be less than three.
Find out more about absolute value inequalities below.
Practice: Solve absolute inequalities in the exercise below.