Solve the inequalities -6 leq 4 - 2x lt 5 - x - JAMB Mathematics 2010 Question

-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