In a right triangle, the side opposite an acute angle has length x, and the hypotenuse has length x + 7. If the sine of that angle is 3/5,…

Sine is the ratio of the opposite side to the hypotenuse, so $\frac{x}{x + 7} = \frac{3}{5}$. Cross-multiply: $5x = 3(x + 7) = 3x + 21$. Subtract $3x$: $2x = 21$, so $x = \frac{21}{2} = 10.5$. Check: the hypotenuse is $17.5$ and $\frac{10.5}{17.5} = 0.6 = \frac{3}{5}$. A common wrong answer is 7, which comes from ignoring the ratio and just reusing the number in the problem. Another is 4.2, from cross-multiplying incorrectly: $5x = 3 \cdot 7 = 21$, forgetting the $x$ in the denominator. Keep the full denominator $x + 7$.