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 :
Answer & explanation
Correct answer: option 3
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:
$x≤\frac{2}{3}$
$-3x+2≥6$
$-3x≥4$
$x≤-\frac{4}{3}$
$⇒\left(-∞,-\frac{4}{3}\right]$