Question

The solution of the inequality $\frac{4x+4}{2}>-x$ is

• A. $(\frac{2}{3},\infty )$
• B. $(-\frac{2}{3},\infty )$
• C. $(-\infty ,\frac{2}{3})$
• D. $(-\infty ,-\frac{2}{3})$

Answer 1

The correct option is B $(-\frac{2}{3},\infty )$

$\frac{4x+4}{2}>-x$
$\Rightarrow 4x+4>-2x$
$\Rightarrow 4>-6x$
$\Rightarrow \frac{2}{3}>-x$
$\Rightarrow x>-\frac{2}{3}\therefore x\in (-\frac{2}{3},\infty )$