{"id":249250,"date":"2024-04-03T06:46:10","date_gmt":"2024-04-03T06:46:10","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/?p=249250"},"modified":"2024-04-03T06:46:10","modified_gmt":"2024-04-03T06:46:10","slug":"how-do-you-solve-absolute-value-inequalities-step-by-step-2","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-solve-absolute-value-inequalities-step-by-step-2\/","title":{"rendered":"How do you solve absolute value inequalities step by step?"},"content":{"rendered":"

Absolute value inequalities can be a little tricky to solve, but with a step-by-step approach, you can master them. So, how do you solve absolute value inequalities step by step? Let’s dive into the process.<\/p>\n

To solve absolute value inequalities, follow these steps:<\/p>\n

Step 1: Write out the inequality
\nWrite the absolute value inequality in the form of |expression| < constant or |expression| > constant.<\/p>\n

Step 2: Split the inequality into two cases
\nSince the absolute value function can result in both positive and negative values, consider both possibilities by splitting the inequality into two separate cases.<\/p>\n

Step 3: Solve the positive case
\nIn the first case, assume that the expression inside the absolute value is positive. Remove the absolute value symbols and rewrite the inequality without them.<\/p>\n

Step 4: Solve the negative case
\nIn the second case, assume that the expression inside the absolute value is negative. Change the inequality symbol and rewrite the inequality without the absolute value.<\/p>\n

Step 5: Simplify and solve
\nSimplify both inequalities obtained from Step 3 and Step 4. Solve each inequality separately, following the regular inequality solving rules.<\/p>\n

Step 6: Combine the solutions
\nOnce you have solved both cases, combine the solutions obtained in Step 5.<\/p>\n

**How do you solve absolute value inequalities step by step?**<\/p>\n

1. Write out the inequality in |expression| < constant or |expression| > constant form.
\n2. Split the inequality into two cases.
\n3. Solve the positive case by removing the absolute value and rewriting the inequality.
\n4. Solve the negative case by changing the inequality symbol and rewriting the inequality.
\n5. Simplify and solve both inequalities.
\n6. Combine the solutions obtained from both cases.<\/p>\n

Now that you know how to solve absolute value inequalities step by step, let’s address some frequently asked questions about this topic:<\/p>\n

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