Question on: JAMB Mathematics - 2010
Solve the inequalities -6 \(\leq\) 4 - 2x < 5 - x
A
-1 < x < 5
B
-1 < x \(\leq\) 5
C
-1 \(\leq\) x \(\leq\) 6
D
-1 \(\leq\) x < 6
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Correct Option: B
-6 \(\leq\) 4 - 2x < 5 - x
split inequalities into two and solve each part as follows:
-6 \(\leq\) 4 - 2x = -6 - 4 \(\leq\) -2x
-10 \(\leq\) -2x
\(\frac{-10}{-2}\) \(\geq\) \(\frac{-2x}{-2}\)
giving 5 \(\geq\) x or x \(\leq\) 5
4 - 2x < 5 - x
-2x + x < 5 - 4
-x < 1
\(\frac{-x}{-1}\) > \(\frac{1}{-1}\)
giving x > -1 or -1 < x
Combining the two results, gives -1 < x \(\leq\) 5
split inequalities into two and solve each part as follows:
-6 \(\leq\) 4 - 2x = -6 - 4 \(\leq\) -2x
-10 \(\leq\) -2x
\(\frac{-10}{-2}\) \(\geq\) \(\frac{-2x}{-2}\)
giving 5 \(\geq\) x or x \(\leq\) 5
4 - 2x < 5 - x
-2x + x < 5 - 4
-x < 1
\(\frac{-x}{-1}\) > \(\frac{1}{-1}\)
giving x > -1 or -1 < x
Combining the two results, gives -1 < x \(\leq\) 5
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