Use interval notation to express the solution set for the inequality below. $| 12 x + 3 |

Question

Use interval notation to express the solution set for the inequality below. $| 12 x + 3 | < 1$
A) $\left( - \infty , - \frac { 1 } { 6 } \right)$
B) $\left[ - \frac { 1 } { 3 } , \infty \right)$
C) $\left( - \frac { 1 } { 3 } , \infty \right)$
D) $\left( - \frac { 1 } { 3 } , - \frac { 1 } { 6 } \right)$
E) $\left( - \infty , - \frac { 1 } { 6 } \right]$

Quizplus · Accepted Answer

To solve $| 12x + 3 | < 1$, we consider two cases: $12x + 3 < 1$ and $12x + 3 > -1$. Solving these gives $x < -\frac{1}{6}$ and $x > -\frac{1}{3}$, respectively. The intersection of these two solutions is $\left( - \frac { 1 } { 3 } , - \frac { 1 } { 6 } \right)$.

Use Interval Notation to Express the Solution Set for the Inequality