<\/span><\/h3>\nTo solve absolute value inequalities, follow these step-by-step instructions:<\/p>\n
Step 1: Isolate the absolute value expression.<\/b>
\n * If the expression inside the absolute value bars is a single variable, isolate it on one side of the inequality.
\n * If the expression inside the absolute value bars is a combination of terms, isolate the absolute value expression by moving all other terms to the opposite side of the inequality.<\/p>\n
Step 2: Break the inequality into two separate equations.<\/b>
\n * Rewrite the inequality as two separate equations, one positive and one negative, by removing the absolute value bars and changing the inequality symbol to an equal sign with a plus or minus symbol.
\n * For example, if the original inequality is |x – 3| < 5, write x - 3 = 5 and x - 3 = -5.\n\n\nStep 3: Solve each equation separately.<\/b>
\n * Solve the two equations separately to find the possible values for the variable.
\n * For example, for x – 3 = 5, add 3 to both sides to get x = 8. And for x – 3 = -5, add 3 to both sides to get x = -2.<\/p>\n
Step 4: Check the solutions.<\/b>
\n * Substitute each solution back into the original inequality to check if it satisfies the inequality.
\n * If a solution satisfies the inequality, it is part of the solution set.<\/p>\n
Step 5: Write the solution set.<\/b>
\n * Combine the solutions from both equations to form the final solution set.
\n * For example, the solution set for |x – 3| < 5 is {-2, 8}.\n\n\n\n\n