Question

Solve the proportion. Check for extraneous solutions. $$\frac{6}{x}=\frac{5}{3}$$

Short answer

The solution to the equation is \(x = 3.6\).

Step-by-step solution

Cross-multiply

Multiply the numerator of the first fraction by the denominator of the second one, and the denominator of the first by the numerator of the second. So,\(6*3 = 5*x\) will yield \(18 = 5x\).

Solving for the unknown

To solve for \(x\), divide each side of the equation by 5. Therefore, \(x = 18/5 = 3.6\).

Check for Extraneous Solution

Substitute the value of \(x\) back into the original equation to check for accuracy. Hence, \(\frac{6}{3.6} = \frac{5}{3}\), simplifying both sides we obtain \(1.67 \approx 1.67\). The left-hand side equals the right-hand side, so the solution is correct.