Question

Solve the proportion. Check for extraneous solutions. $$\frac{16}{4}=\frac{12}{x}$$

Short answer

The solution of the proportion \(\frac{16}{4} = \frac{12}{x}\) is \(x = 3\). There are no extraneous solutions.

Step-by-step solution

Cross-multiplication

Cross-multiply the equation \(\frac{16}{4} = \frac{12}{x}\) to get \(16*x = 4*12\).

Simplify the equation

After multiplication, the equation becomes \(16x = 48\).

Isolate x

To isolate \(x\), we need to divide every term of the equation by 16 to get \(x = \frac{48}{16}\).

Simplify the value of x

When you simplify \(x = \frac{48}{16}\), you get \(x = 3\).

Check for extraneous solutions

To verify that \(x = 3\) is not an extraneous solution, substitute \(x\) by 3 in the original equation to ensure that the both sides are equal. Doing this, we have \(\frac{16}{4} = \frac{12}{3}\), which simplifies to 4=4, confirming that 3 is a valid solution, and there are no extraneous solutions.