Solve the compound inequality. Write the solution in interval notation.
- $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 }

Question

Solve the compound inequality. Write the solution in interval notation.
-  $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }$
A) $\left[ - \frac { 5 } { 21 } , \frac { 1 } { 3 } \right]$
B) $\left[ - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right)$
C) $\left( - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right)$
D) $\left( - \frac { 1 } { 7 } , \frac { 3 } { 7 } \right]$

Quizplus · Accepted Answer

To solve the compound inequality $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }$, we first multiply all parts by 6 to eliminate the fraction: $-2 \leq 7x - 1 < 2$. Then, we add 1 to all parts: $-1 \leq 7x < 3$. Finally, we divide all parts by 7: $-\frac{1}{7} \leq x < \frac{3}{7}$, which matches the interval notation in choice B.

Solve the Compound Inequality −13≤7x−16<13- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }−31​≤67x−1​<31​

Solve the Compound Inequality $- \frac { 1 } { 3 } \leq \frac { 7 x - 1 } { 6 } < \frac { 1 } { 3 }$