Question

Solve the inequality with absolute value
$-3|-2x+4|<=4$

• A. $(-\infty ,\frac{7}{3})$
• B. $(\frac{7}{3},+\infty )$
• C. $(\frac{7}{3},+\frac{7}{3})$
• D. $(0,\frac{7}{3})$
• E. $(-\infty ,+\infty )$

Answer 1

The correct option is E $(-\infty ,+\infty )$

Since $|x|=x$ and $-x$,

therefore, $-3|-2x+4|<=4$ may be calculated as:

$-3(-2x+4)<=4$ and $3(-2x+4)<=4$

$\Rightarrow 6x-12<=4$ and $-6x+12<=4$

$\Rightarrow 6x<=4+12$ and $-6x<=4-12$

$\Rightarrow x<=\frac{8}{3}$ and $x>=\frac{4}{3}$

Therefore, $x$ lies between $(-\infty ,+\infty )$.

Hence, option E is correct.