<\/span><\/h3>\nTo illustrate the process, let’s solve the inequality |x + 3| < 5:\n\n\nStep 1: Set up the inequality
\nRemove the absolute value symbols:
\nx + 3 < 5 and -(x + 3) < 5\n\n\nStep 2: Solve the separate inequalities
\nFor x + 3 < 5:
\nx < 2\n\n\nFor -(x + 3) < 5:
\n-x – 3 < 5
\n-x < 8
\nx > -8<\/p>\n
Step 3: Analyze the solutions
\nCombine the solution sets: x < 2 or x > -8<\/p>\n
<\/span>Frequently Asked Questions (FAQs)<\/span><\/h2>\n<\/span>What happens when there is an equal sign in the absolute value inequality?<\/span><\/h3>\n\nWhen there is an equal sign, the “less than or equal to” and “greater than or equal to” signs should be used in the separate inequalities.<\/p>\n
<\/span>How do you solve absolute value inequalities with fractions?<\/span><\/h3>\n\nTo solve an absolute value inequality with fractions, treat the fraction as any other expression. Find the critical points where the expression changes sign, and test intervals to determine the solution.<\/p>\n
<\/span>Can an absolute value inequality have no solution?<\/span><\/h3>\n\nYes, it is possible for an absolute value inequality to have no solution if the absolute value expression cannot satisfy the given inequality.<\/p>\n