Question

Solve the inequality $\frac{3-x}{x+2}$ > 1

• A. - 2 < x < 0
• B. -2 < x < 3
• C.
• D. -1 < x < 3

Answer 1

The correct option is C

$\frac{3-x}{x+2}$ > 1

$\frac{3-x}{x+2}$ - 1 > 0

$\frac{3-x-x-2}{x+2}$ > 0

$\frac{1-2x}{x+2}$ > 0

$\frac{2x-1}{x+2}$ < 0

2x - 1 < 0 x + 2 > 0

x < $\frac{1}{2}$ x > -2

Draw the number line for these two inequalities. We get,

Common part -2 < x < $\frac{1}{2}$