QuestionJuly 15, 2025

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

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

Solution
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Answer

x = -6 Explanation 1. Eliminate Fractions Multiply every term by 15 (LCM of 3 and 5) to eliminate fractions: 15 \cdot \frac{2x}{3} - 15 \cdot \frac{2x+4}{5} = 15 \cdot \frac{2x}{5}. 2. Simplify Each Term Simplify: 10x - 3(2x + 4) = 6x. 3. Distribute and Combine Like Terms Distribute: 10x - 6x - 12 = 6x. Combine like terms: 4x - 12 = 6x. 4. Solve for x Subtract 4x from both sides: -12 = 2x. Divide by 2: x = -6.

Explanation

1. Eliminate Fractions<br /> Multiply every term by 15 (LCM of 3 and 5) to eliminate fractions: $15 \cdot \frac{2x}{3} - 15 \cdot \frac{2x+4}{5} = 15 \cdot \frac{2x}{5}$.<br /><br />2. Simplify Each Term<br /> Simplify: $10x - 3(2x + 4) = 6x$.<br /><br />3. Distribute and Combine Like Terms<br /> Distribute: $10x - 6x - 12 = 6x$. Combine like terms: $4x - 12 = 6x$.<br /><br />4. Solve for x<br /> Subtract $4x$ from both sides: $-12 = 2x$. Divide by 2: $x = -6$.
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