Questions: Solve the following equation 4/x = 16/12

Transcript text: Solve the following equation \[ \frac{4}{x}=\frac{16}{12} \]

Solution

Solution Steps

To solve the equation \(\frac{4}{x} = \frac{16}{12}\), we can cross-multiply to eliminate the fractions and solve for \(x\). This involves multiplying both sides of the equation by \(x\) and then by 12, simplifying the resulting equation, and solving for \(x\).

Step 1: Set Up the Equation

We start with the equation \(\frac{4}{x} = \frac{16}{12}\). Simplifying the right side, we have \(\frac{16}{12} = \frac{4}{3}\). Thus, the equation becomes: \[ \frac{4}{x} = \frac{4}{3} \]

Step 2: Cross-Multiply

To eliminate the fractions, we cross-multiply: \[ 4 \cdot 3 = 4 \cdot x \] This simplifies to: \[ 12 = 4x \]

Step 3: Solve for \(x\)

Divide both sides by 4 to solve for \(x\): \[ x = \frac{12}{4} = 3 \]