Absolute Value Inequalities

Steps to solve inequalities with absolute value:

1. Isolate the absolute value expression on the left side of the inequality.
2. If the number on the other side of the inequality sign is negative, your equation either has no solution or all real numbers as solutions. Use the sign of each side of your inequality to decide which of these cases holds.
3. Remove the absolute value operators by setting up a compound inequality. The type of inequality sign in the problem will tell us the way we set up the compound inequality.
4. Solve the inequalities.

Question 1: Solve the inequality ∣x - 5∣ < x2 + 3

Question 2: Solve the inequality ∣x2 + 5∣ > 5

Question 3: Solve the inequality ∣x∣ < x - 2

Question 4: Solve the inequality ∣9 - 2x∣ < 15

Question 5: Solve the inequality 5 + 2∣x∣ < 17

Question 6: Solve the inequality ∣x2 - 1∣ < 24

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