Solving Absolute Value Inequalities

Students learn that when solving an absolute value inequality, such as 5 I x + 3 I > 20, the first step is to isolate the absolute value by dividing both sides of the equation by 5 to get I x + 3 I > 4. The next step is to split the equation up into two separate equations in the following way: x + 3 > 4 or x + 3 < -4. Notice that in the second equation, the inequality sign switches and the 4 becomes negative. Also notice that "or" is used between the two equations, because the absolute value equation used a "greater than" sign: I x + 3 I > 4. If the absolute value equation had used a "less than" sign, then "and" would have been used between the two equations.