QuestionAugust 26, 2025

(x)/(7)+(x)/(3)=(3)/(14)

(x)/(7)+(x)/(3)=(3)/(14)
(x)/(7)+(x)/(3)=(3)/(14)

Solution
4.2(274 votes)

Answer

x = \frac{63}{140} Explanation 1. Find a common denominator for the fractions The least common multiple of 7 and 3 is 21. Rewrite each fraction with this common denominator: \frac{x}{7} = \frac{3x}{21} and \frac{x}{3} = \frac{7x}{21}. 2. Combine the fractions on the left side Add the fractions: \frac{3x}{21} + \frac{7x}{21} = \frac{10x}{21}. 3. Set up the equation The equation becomes \frac{10x}{21} = \frac{3}{14}. 4. Cross-multiply to solve for x Cross-multiplying gives 10x \cdot 14 = 3 \cdot 21. 5. Simplify and solve for x Calculate: 140x = 63. Divide both sides by 140: x = \frac{63}{140}.

Explanation

1. Find a common denominator for the fractions<br /> The least common multiple of 7 and 3 is 21. Rewrite each fraction with this common denominator: $\frac{x}{7} = \frac{3x}{21}$ and $\frac{x}{3} = \frac{7x}{21}$.<br /><br />2. Combine the fractions on the left side<br /> Add the fractions: $\frac{3x}{21} + \frac{7x}{21} = \frac{10x}{21}$.<br /><br />3. Set up the equation<br /> The equation becomes $\frac{10x}{21} = \frac{3}{14}$.<br /><br />4. Cross-multiply to solve for $x$<br /> Cross-multiplying gives $10x \cdot 14 = 3 \cdot 21$.<br /><br />5. Simplify and solve for $x$<br /> Calculate: $140x = 63$. Divide both sides by 140: $x = \frac{63}{140}$.
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