QuestionAugust 24, 2025

6. Solve the absolute value equation: vert 3b+4vert -8=20

6. Solve the absolute value equation: vert 3b+4vert -8=20
6. Solve the absolute value equation: vert 3b+4vert -8=20

Solution
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Answer

b = 8, -\frac{32}{3} Explanation 1. Isolate the Absolute Value Add 8 to both sides: \vert 3b+4 \vert = 28. 2. Solve for Two Cases Case 1: 3b + 4 = 28. Subtract 4 from both sides: 3b = 24. Divide by 3: b = 8. Case 2: 3b + 4 = -28. Subtract 4 from both sides: 3b = -32. Divide by 3: b = -\frac{32}{3}.

Explanation

1. Isolate the Absolute Value<br /> Add 8 to both sides: $\vert 3b+4 \vert = 28$.<br /><br />2. Solve for Two Cases<br /> Case 1: $3b + 4 = 28$. Subtract 4 from both sides: $3b = 24$. Divide by 3: $b = 8$.<br /> Case 2: $3b + 4 = -28$. Subtract 4 from both sides: $3b = -32$. Divide by 3: $b = -\frac{32}{3}$.
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