Question
Question 27 Solve: \( |x+7|>3 \) Give your answer as an interval.
Ask by Mccarthy Flynn. in the United States
Feb 04,2025
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Answer
The solution is \( x < -10 \) or \( x > -4 \).
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Mind Expander
To solve the inequality \( |x+7|>3 \), we need to consider two separate cases based on the definition of absolute value. 1. The first case is when \( x + 7 > 3 \): - Subtracting 7 from both sides, we get \( x > -4 \). 2. The second case is when \( x + 7 < -3 \): - Subtracting 7 from both sides, we find \( x < -10 \). Combining both results, the solution in interval notation is: \( (-\infty, -10) \cup (-4, \infty) \).
