Question
Find the solution set for the following inequality. \[ |2 x-13|>11 \]
Ask by Hammond Stanley. in the United States
Feb 04,2025
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The solution set for the inequality \( |2x-13|>11 \) is all real numbers less than 1 and greater than 12.
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Mind Expander
To solve the inequality \( |2x - 13| > 11 \), we need to consider the two cases that arise from the absolute value. **Case 1:** \( 2x - 13 > 11 \) Adding 13 to both sides gives: \( 2x > 24 \) Dividing by 2 yields: \( x > 12 \) **Case 2:** \( 2x - 13 < -11 \) Adding 13 to both sides gives: \( 2x < 2 \) Dividing by 2 yields: \( x < 1 \) Combining both cases, the solution set is: \( x < 1 \) or \( x > 12 \). In interval notation, this is: \( (-\infty, 1) \cup (12, \infty) \).
