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Solve the following inequality and give the solution in interval notation. \( 5 s-3>2 \) or \( 2 s-1 \leq 7 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set in interval notation is B. The solution set is the empty set.

Ask by Macdonald Fitzgerald. in the United States
Feb 04,2025

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The solution set in interval notation is \( (-\infty, \infty) \).

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The Deep Dive

To solve the inequality \( 5s - 3 > 2 \): 1. Add 3 to both sides: \( 5s > 5 \) 2. Divide by 5: \( s > 1 \) Now, for the second inequality \( 2s - 1 \leq 7 \): 1. Add 1 to both sides: \( 2s \leq 8 \) 2. Divide by 2: \( s \leq 4 \) Now, we combine the solutions from both inequalities. The first inequality gives \( s > 1 \), while the second gives \( s \leq 4 \). Thus, the solution set in interval notation is: \( (1, 4] \) So, the correct choice is: A. The solution set in interval notation is \( (1, 4] \).

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