Solve the inequality. Express your answer using interval notation.
-$$| 8 \mathrm { k } - 2 | \leq 7$$
A) $\left( - \infty , - \frac { 5 } { 8 } \right] \cup \left[ \frac { 9 } { 8 } , \infty \right)$
B) $\left[ - \infty , \frac { 9 } { 8 } \right]$
C) $\left[ - \frac { 5 } { 8 } , \frac { 9 } { 8 } \right]$
D) $\left( - \frac { 5 } { 8 } , \frac { 9 } { 8 } \right)$

Question

Quizplus · Accepted Answer

To solve the inequality $| 8k - 2 | \leq 7$, we break it into two cases: $8k - 2 \leq 7$ and $8k - 2 \geq -7$. Solving the first gives $8k \leq 9$, so $k \leq \frac{9}{8}$. Solving the second gives $8k \geq -5$, so $k \geq -\frac{5}{8}$. Combining these gives the solution $\left[ - \frac { 5 } { 8 } , \frac { 9 } { 8 } \right]$.

Solve the Inequality ∣8k−2∣≤7| 8 \mathrm { k } - 2 | \leq 7∣8k−2∣≤7

Solve the Inequality $| 8 \mathrm { k } - 2 | \leq 7$