Solve the inequality.Express the solution set in interval notation. $$| 3 x - 2 |

Question

Solve the inequality.Express the solution set in interval notation. $$| 3 x - 2 | < 5$$
A) $\quad ( 3,7 )$
B)$$
\left(-1, \frac{3}{7}\right)
$$
C) $\left( - 1 , \frac { 7 } { 3 } \right)$
D) $\quad \left( 1 , \frac { 7 } { 3 } \right)$
E) $\left( - \infty , - \frac { 7 } { 3 } \right) \cup ( - 1 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $| 3x - 2 | < 5$, we split it into two cases: $3x - 2 < 5$ and $3x - 2 > -5$. Solving the first gives $3x < 7$, or $x < \frac{7}{3}$. Solving the second gives $3x > -3$, or $x > -1$. Combining these gives the solution $\left( - 1 , \frac { 7 } { 3 } \right)$.

Solve the Inequality ∣3x−2∣<5| 3 x - 2 | < 5∣3x−2∣<5

Solve the Inequality $| 3 x - 2 | < 5$