Description

In the SAT Math section, questions involving the absolute value of linear inequalities often test a student’s understanding of how to manipulate and solve equations with absolute values. When dealing with absolute values in inequalities, it’s crucial to understand that the absolute value of a number represents its distance from zero on the number line. For example, |x – 3| represents the distance between x and 3.

In solving absolute value inequalities, one typically considers two cases: when the expression inside the absolute value is positive and when it’s negative. For instance, for |x – 3| < 5, one would solve both x – 3 < 5 and -(x – 3) < 5 to find the possible values of x. The resulting solution set may involve intervals on the number line, where x can take on any value within those intervals to satisfy the inequality. Graphical representations are often helpful in visualizing these solutions.

Students may encounter questions requiring them to solve absolute value inequalities, interpret solutions, or apply them in real-world scenarios. Understanding the properties and methods for solving absolute value inequalities is crucial for success in such SAT questions.  An expression using absolute value and inequality signs is known as an absolute value inequality. A larger than sign is included in the absolute value inequality |x + 3| > 1 for one case.