QuestionJune 24, 2025

7. (2x)/(3)+(3x)/(5)=(x)/(3)+(14)/(3)

7. (2x)/(3)+(3x)/(5)=(x)/(3)+(14)/(3)
7.
(2x)/(3)+(3x)/(5)=(x)/(3)+(14)/(3)

Solution
3.2(335 votes)

Answer

x = 5 Explanation 1. Combine like terms on the left \frac{2x}{3} + \frac{3x}{5} = \frac{10x}{15} + \frac{9x}{15} = \frac{19x}{15} 2. Simplify the right side \frac{x}{3} + \frac{14}{3} = \frac{x + 14}{3} 3. Clear fractions by multiplying through by 15 15 \cdot \frac{19x}{15} = 15 \cdot \frac{x + 14}{3} 4. Solve for x 19x = 5(x + 14) 19x = 5x + 70 19x - 5x = 70 14x = 70 x = \frac{70}{14} = 5

Explanation

1. Combine like terms on the left<br /> $\frac{2x}{3} + \frac{3x}{5} = \frac{10x}{15} + \frac{9x}{15} = \frac{19x}{15}$<br /><br />2. Simplify the right side<br /> $\frac{x}{3} + \frac{14}{3} = \frac{x + 14}{3}$<br /><br />3. Clear fractions by multiplying through by 15<br /> $15 \cdot \frac{19x}{15} = 15 \cdot \frac{x + 14}{3}$<br /><br />4. Solve for x<br /> $19x = 5(x + 14)$<br /> $19x = 5x + 70$<br /> $19x - 5x = 70$<br /> $14x = 70$<br /> $x = \frac{70}{14} = 5$
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