WAEC SSCE - General Mathematics - 2008 (Objective)

Question 1 Report

If p = $\frac{1}{2}$ and $\frac{1}{p - 1} = \frac{2}{p + x}$, find the value of x

-2$\frac{1}{2}$

-1$\frac{1}{2}$ Correct answer

1$\frac{1}{2}$

2$\frac{1}{2}$

Answer Details

Given that p = $\frac{1}{2}$ and $\frac{1}{p - 1} = \frac{2}{p + x}$, we want to find the value of x. We can start by substituting the value of p in the second equation: \begin{aligned} \frac{1}{p - 1} &= \frac{2}{p + x} \\ \\ \frac{1}{\frac{1}{2} - 1} &= \frac{2}{\frac{1}{2} + x} && \text{(Substitute } p = \frac{1}{2} \text{)}\\ \\ \frac{1}{-\frac{1}{2}} &= \frac{2}{\frac{1}{2} + x} && \text{(Simplify)}\\ \\ -2 &= \frac{2}{\frac{1}{2} + x} && \text{(Simplify)}\\ \\ -2\left(\frac{1}{2} + x\right) &= 2 && \text{(Cross-multiply)}\\ \\ -1 - 2x &= 1 && \text{(Simplify)}\\ \\ -2x &= 2 \\ \\ x &= -1 \end{aligned} Therefore, the value of x is -1.5, which corresponds to option B: -1$\frac{1}{2}$.






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