5. M/J 16/P21/Q2/a, \( \mathbf{d}(\mathrm{ii}) \) (a) Solve the equation \( \frac{p-1}{7-p}=5 \)

Solve the equation \( \frac{p-1}{7-p}=5 \). Solve the equation by following steps: - step0: Solve for \(p\): \(\frac{p-1}{7-p}=5\) - step1: Find the domain: \(\frac{p-1}{7-p}=5,p\neq 7\) - step2: Cross multiply: \(p-1=\left(7-p\right)\times 5\) - step3: Simplify the equation: \(p-1=5\left(7-p\right)\) - step4: Expand the expression: \(p-1=35-5p\) - step5: Move the expression to the left side: \(p+5p=35+1\) - step6: Add and subtract: \(6p=35+1\) - step7: Add and subtract: \(6p=36\) - step8: Divide both sides: \(\frac{6p}{6}=\frac{36}{6}\) - step9: Divide the numbers: \(p=6\) - step10: Check if the solution is in the defined range: \(p=6,p\neq 7\) - step11: Find the intersection: \(p=6\) The solution to the equation \( \frac{p-1}{7-p}=5 \) is \( p=6 \).