Solve the inequality. Express your answer using interval notation.
-$| 7 k - 7 | - 2

Question

Solve the inequality. Express your answer using interval notation.
-$| 7 k - 7 | - 2 < 6$
A) $\left( - \infty , - \frac { 1 } { 7 } \right)$
B) $\left( - \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$
C) $\left( - \infty , \frac { 15 } { 7 } \right)$
D) $\left( - \infty , - \frac { 1 } { 7 } \right) \cup \left( \frac { 15 } { 7 } , \infty \right)$

Quizplus · Accepted Answer

First, simplify the inequality: $| 7k - 7 | - 2 < 6$ becomes $| 7k - 7 | < 8$. This can be split into two cases: $7k - 7 < 8$ and $7k - 7 > -8$. Solving these gives $k < \frac{15}{7}$ and $k > -\frac{1}{7}$, respectively. Combining these gives the solution interval $\left( - \frac { 1 } { 7 } , \frac { 15 } { 7 } \right)$.

Solve the Inequality ∣7k−7∣−2<6| 7 k - 7 | - 2 < 6∣7k−7∣−2<6

Solve the Inequality $| 7 k - 7 | - 2 < 6$