Solution set for the inequality $\left|\frac{3x-2}{2}\right|≥3$ includes the intervals :

A. $\left(\frac{8}{3}, ∞\right)$

B. $\left[\frac{8}{3}, ∞\right)$

C. $\left[\frac{4}{3}, ∞\right)$

D. $\left(\frac{4}{3}, ∞\right)$

E. $\left(-∞, \frac{-4}{3}\right]$

Choose the correct answer from the options given below :

B and E only

The correct answer is Option (3) → B and E only

$\left|\frac{3x-2}{2}\right|≥3$

$|3x-2|≥6$

Case 1:

$x≥\frac{2}{3}$

$3x-2≥6$

$3x≥8$

$x≥\frac{8}{3}$

$⇒\left[\frac{2}{3},∞\right)$

Case 2:

$x≤\frac{2}{3}$

$-3x+2≥6$

$-3x≥4$

$x≤-\frac{4}{3}$

$⇒\left(-∞,-\frac{4}{3}\right]$