WAEC - Mathematics (2008 - No. 27)
If p = \(\frac{1}{2}\) and \(\frac{1}{p - 1} = \frac{2}{p + x}\), find the value of x
-2\(\frac{1}{2}\)
-1\(\frac{1}{2}\)
1\(\frac{1}{2}\)
2\(\frac{1}{2}\)
Explanation
p = \(\frac{1}{2}; \frac{1}{p - 1} = \frac{2}{p + x}\)
\(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\)
\(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
\(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
-2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\)
1 + 2x = \(\frac{4}{-2}\)
1 + 2x = -2
2x = -2 - 1
2x = -3
x = -\(\frac{3}{2}\)
x = -1\(\frac{1}{2}\)
\(\frac{1}{\frac{1}{2} - 1} = \frac{2}{\frac{1}{2} + x}\)
\(\frac{1}{\frac{1 - 2}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
\(\frac{1}{-\frac{1}{2}} = \frac{2}{\frac{1 + 2x}{2}}\)
-2 = \(\frac{4}{1 + 2x} -2(1 + 2x) = 4\)
1 + 2x = \(\frac{4}{-2}\)
1 + 2x = -2
2x = -2 - 1
2x = -3
x = -\(\frac{3}{2}\)
x = -1\(\frac{1}{2}\)
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