Solve the inequality. Write the answer in interval notation.
-$| 7 x + 6 | \geq 7$
A) $\left[ - \frac { 13 } { 7 } , \frac { 1 } { 7 } \right]$
B) $\left[ \frac { 1 } { 7 } , \infty \right)$
C) $\left( - \frac { 13 } { 7 } , \frac { 1 } { 7 } \right)$
D) $\left( - \infty , - \frac { 13 } { 7 } \right] \cup \left[ \frac { 1 } { 7 } , \infty \right)$

Question

Quizplus · Accepted Answer

To solve $| 7x + 6 | \geq 7$, we consider two cases: $7x + 6 \geq 7$ and $7x + 6 \leq -7$. Solving the first gives $x \geq \frac{1}{7}$ and the second gives $x \leq -\frac{13}{7}$. Thus, the solution is $x \leq -\frac{13}{7}$ or $x \geq \frac{1}{7}$, which in interval notation is $\left( - \infty , - \frac { 13 } { 7 } \right] \cup \left[ \frac { 1 } { 7 } , \infty \right)$.

Solve the Inequality ∣7x+6∣≥7| 7 x + 6 | \geq 7∣7x+6∣≥7

Solve the Inequality $| 7 x + 6 | \geq 7$