QuestionJuly 15, 2025

(4) (3x-1)/(2)=(4x-3)/(3)+(5)/(6)

(4) (3x-1)/(2)=(4x-3)/(3)+(5)/(6)
(4) (3x-1)/(2)=(4x-3)/(3)+(5)/(6)

Solution
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Answer

x = 2 Explanation 1. Eliminate Fractions Multiply every term by 6 to eliminate fractions: 6 \cdot \frac{3x-1}{2} = 6 \cdot \frac{4x-3}{3} + 6 \cdot \frac{5}{6}. 2. Simplify Each Term Simplify: 3(3x - 1) = 2(4x - 3) + 5. 3. Expand and Simplify Expand: 9x - 3 = 8x - 6 + 5. 4. Combine Like Terms Simplify: 9x - 3 = 8x - 1. 5. Solve for x Subtract 8x from both sides: x - 3 = -1. Add 3 to both sides: x = 2.

Explanation

1. Eliminate Fractions<br /> Multiply every term by 6 to eliminate fractions: $6 \cdot \frac{3x-1}{2} = 6 \cdot \frac{4x-3}{3} + 6 \cdot \frac{5}{6}$.<br /><br />2. Simplify Each Term<br /> Simplify: $3(3x - 1) = 2(4x - 3) + 5$.<br /><br />3. Expand and Simplify<br /> Expand: $9x - 3 = 8x - 6 + 5$.<br /><br />4. Combine Like Terms<br /> Simplify: $9x - 3 = 8x - 1$.<br /><br />5. Solve for x<br /> Subtract $8x$ from both sides: $x - 3 = -1$. Add 3 to both sides: $x = 2$.
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