Solve the inequality. Express your answer using interval notation.
-$$| 5 \mathrm { k } + 3 | + 6 10$$
A) $\left( \frac { 1 } { 5 } , \infty \right)$
B) $\left( - \frac { 7 } { 5 } , \frac { 1 } { 5 } \right)$
C) $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$
D) $\left( - \infty , - \frac { 7 } { 5 } \right] \cup \left[ \frac { 1 } { 5 } , \infty \right)$

Question

Solve the inequality. Express your answer using interval notation.
-$$| 5 \mathrm { k } + 3 | + 6 > 10$$
A) $\left( \frac { 1 } { 5 } , \infty \right)$
B) $\left( - \frac { 7 } { 5 } , \frac { 1 } { 5 } \right)$
C) $\left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$
D) $\left( - \infty , - \frac { 7 } { 5 } \right] \cup \left[ \frac { 1 } { 5 } , \infty \right)$

Quizplus · Accepted Answer

First, simplify the inequality: $| 5k + 3 | + 6 > 10 \Rightarrow | 5k + 3 | > 4$. This leads to two cases: $5k + 3 > 4$ and $5k + 3 < -4$. Solving these gives $k > \frac{1}{5}$ and $k < -\frac{7}{5}$, respectively. Thus, the solution is $k \in \left( - \infty , - \frac { 7 } { 5 } \right) \cup \left( \frac { 1 } { 5 } , \infty \right)$.

Solve the Inequality ∣5k+3∣+6>10| 5 \mathrm { k } + 3 | + 6 > 10∣5k+3∣+6>10

Solve the Inequality $| 5 \mathrm { k } + 3 | + 6 > 10$