{"id":212490,"date":"2024-03-24T12:05:44","date_gmt":"2024-03-24T12:05:44","guid":{"rendered":"https:\/\/namso-gen.co\/blog\/how-do-you-write-an-absolute-value-inequality\/"},"modified":"2024-03-24T12:05:44","modified_gmt":"2024-03-24T12:05:44","slug":"how-do-you-write-an-absolute-value-inequality","status":"publish","type":"post","link":"https:\/\/namso-gen.co\/blog\/how-do-you-write-an-absolute-value-inequality\/","title":{"rendered":"How do you write an absolute value inequality?"},"content":{"rendered":"

Absolute value inequalities involve the use of absolute value in mathematical expressions and equations. To write an absolute value inequality, follow these steps:<\/p>\n

1. Start by identifying the absolute value expression in the problem.
\n2. Set up the expression as a greater than or less than statement.
\n3. Consider two scenarios: one when the expression is positive and one when it is negative.
\n4. Write the two separate inequalities based on these scenarios.
\n5. Simplify both inequalities to find the solution set.<\/p>\n

To understand this process better, let’s consider an example:<\/p>\n

Example:<\/strong>
\nWrite the absolute value inequality for the expression |2x – 3| > 5.<\/p>\n

Solution:<\/strong>
\nStep 1:
\nIdentify the absolute value expression: 2x – 3.<\/p>\n

Step 2:
\nSetup the greater than statement: 2x – 3 > 5.<\/p>\n

Step 3:
\nConsider both cases:
\nWhen 2x – 3 is positive: 2x – 3 > 5.
\nWhen 2x – 3 is negative: -(2x – 3) > 5.<\/p>\n

Step 4:
\nSimplify the inequalities:
\nFor the positive case: 2x – 3 > 5 –> 2x > 8 –> x > 4.
\nFor the negative case: -(2x – 3) > 5 –> -2x + 3 > 5 –> -2x > 2 –> x < -1.\n\n\nStep 5:
\nCombine the solutions from both cases: x < -1 or x > 4.<\/p>\n

Therefore, the solution to the absolute value inequality |2x – 3| > 5 is x < -1 or x > 4.<\/p>\n

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