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