5) \( \frac{2}{3}=\frac{x}{6} \quad ; \frac{8}{2}=\frac{28}{x} \)

Solve the equation \( \frac{2}{3}=\frac{x}{6} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{2}{3}=\frac{x}{6}\) - step1: Swap the sides: \(\frac{x}{6}=\frac{2}{3}\) - step2: Multiply both sides of the equation by \(6:\) \(\frac{x}{6}\times 6=\frac{2}{3}\times 6\) - step3: Multiply the terms: \(x=\frac{2\times 6}{3}\) - step4: Evaluate: \(x=4\) Solve the equation \( \frac{8}{2}=\frac{28}{x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{8}{2}=\frac{28}{x}\) - step1: Find the domain: \(\frac{8}{2}=\frac{28}{x},x\neq 0\) - step2: Divide the terms: \(4=\frac{28}{x}\) - step3: Swap the sides: \(\frac{28}{x}=4\) - step4: Cross multiply: \(28=x\times 4\) - step5: Simplify the equation: \(28=4x\) - step6: Rewrite the expression: \(4\times 7=4x\) - step7: Evaluate: \(7=x\) - step8: Swap the sides: \(x=7\) - step9: Check if the solution is in the defined range: \(x=7,x\neq 0\) - step10: Find the intersection: \(x=7\) The solutions to the given equations are: 1. \( x = 4 \) 2. \( x = 7 \)