Question:
Solve for \( x \):
\[
\frac{2}{x} + \frac{3}{x} = \frac{10}{15}
\]
Solve for \( x \):
\[
\frac{2}{x} + \frac{3}{x} = \frac{10}{15}
\]
Show Hint
For equations involving fractions, simplify and cross-multiply to eliminate the fractions.
Updated On: Oct 6, 2025
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The Correct Option is C
Solution and Explanation
The given equation is:
\[
\frac{2}{x} + \frac{3}{x} = \frac{10}{15}.
\]
Simplify the left side by combining the fractions:
\[
\frac{2 + 3}{x} = \frac{10}{15}
\Rightarrow
\frac{5}{x} = \frac{2}{3}. \] Now, cross-multiply: \[ 5 \times 3 = 2 \times x
\Rightarrow
15 = 2x. \] Finally, solve for \( x \): \[ x = \frac{15}{2} = 7.5. \] Thus, the value of \( x \) is \( \boxed{7.5} \).
\Rightarrow
\frac{5}{x} = \frac{2}{3}. \] Now, cross-multiply: \[ 5 \times 3 = 2 \times x
\Rightarrow
15 = 2x. \] Finally, solve for \( x \): \[ x = \frac{15}{2} = 7.5. \] Thus, the value of \( x \) is \( \boxed{7.5} \).
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