Solve the compound inequality. Give the answer in interval notation.
-$- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 6 }

Question

Solve the compound inequality. Give the answer in interval notation.
-$- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 6 } < \frac { 1 } { 3 }$
A) $\left( - \frac { 1 } { 3 } , 1 \right]$
B) $\left( - \frac { 1 } { 3 } , 1 \right)$
C) $\left[ - \frac { 1 } { 3 } , 1 \right)$
D) $\left[ - \frac { 5 } { 9 } , \frac { 7 } { 9 } \right)$

Quizplus · Accepted Answer

To solve the compound inequality $- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 6 } < \frac { 1 } { 3 }$, we first multiply all parts by 6 to eliminate the fraction: $-2 \leq 3x - 1 < 2$. Then, we add 1 to all parts: $-1 \leq 3x < 3$. Finally, we divide all parts by 3: $-\frac{1}{3} \leq x < 1$, which corresponds to the interval notation $\left[ - \frac { 1 } { 3 } , 1 \right)$.

Solve the Compound Inequality −13≤3x−16<13- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 6 } < \frac { 1 } { 3 }−31​≤63x−1​<31​

Solve the Compound Inequality $- \frac { 1 } { 3 } \leq \frac { 3 x - 1 } { 6 } < \frac { 1 } { 3 }$