Question
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Tutor-Verified Answer
Answer
The solution set is {3, 5}.
Solution
We start with the equation:
4|2x – 8| + 5 = 13
Step 1: Subtract 5 from both sides:
4|2x – 8| = 13 – 5
4|2x – 8| = 8
Step 2: Divide both sides by 4:
|2x – 8| = 2
Step 3: Solve the absolute value equation by splitting it into two cases:
Case 1: 2x – 8 = 2
2x = 10
x = 5
Case 2: 2x – 8 = -2
2x = 6
x = 3
Thus, the solution set is {3, 5}.
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Simplify this solution Beyond the Answer
To solve the equation \( 4|2x - 8| + 5 = 13 \), start by isolating the absolute value. Subtract 5 from both sides to get \( 4|2x - 8| = 8 \). Dividing both sides by 4 yields \( |2x - 8| = 2 \). Now we have two cases to consider: 1. \( 2x - 8 = 2 \) leads to \( 2x = 10 \) or \( x = 5 \). 2. \( 2x - 8 = -2 \) leads to \( 2x = 6 \) or \( x = 3 \). Thus, the solution set is \( \{3, 5\} \).
