Solve the inequality. Express your answer using interval notation.
-$$| 2 \mathrm { k } - 8 | \geq 9$$
A) $\left[ - \frac { 1 } { 2 } , \frac { 17 } { 2 } \right]$
B) $\left[ \frac { 17 } { 2 } , \infty \right)$
C) $\left( - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 17 } { 2 } , \infty \right)$
D) $\left( - \frac { 1 } { 2 } , \frac { 17 } { 2 } \right)$

Question

Quizplus · Accepted Answer

To solve the inequality $| 2k - 8 | \geq 9$, we consider two cases: $2k - 8 \geq 9$ and $2k - 8 \leq -9$. Solving these gives $k \geq \frac{17}{2}$ and $k \leq -\frac{1}{2}$, respectively. Thus, the solution is $\left( - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 17 } { 2 } , \infty \right)$.

Solve the Inequality ∣2k−8∣≥9| 2 \mathrm { k } - 8 | \geq 9∣2k−8∣≥9

Solve the Inequality $| 2 \mathrm { k } - 8 | \geq 9$