Solve and write interval notation for the solution set.
-$$| 3 x - 7 | - 6$$
A) No solution
B) $( - \infty , \infty )$
C) $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( - \frac { 11 } { 3 } , \infty \right)$
D) $\left( - \infty , \frac { 13 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$

Question

Solve and write interval notation for the solution set.
-$$| 3 x - 7 | > - 6$$
A) No solution
B) $( - \infty , \infty )$
C) $\left( - \infty , \frac { 1 } { 3 } \right) \cup \left( - \frac { 11 } { 3 } , \infty \right)$
D) $\left( - \infty , \frac { 13 } { 3 } \right) \cup \left( \frac { 1 } { 3 } , \infty \right)$

Quizplus · Accepted Answer

The inequality $| 3x - 7 | > -6$ is always true because the absolute value of any real number is always non-negative, meaning it's always greater than any negative number. Therefore, the solution set includes all real numbers, represented by $(- \infty, \infty)$.

Solve and Write Interval Notation for the Solution Set ∣3x−7∣>−6| 3 x - 7 | > - 6∣3x−7∣>−6

Solve and Write Interval Notation for the Solution Set $| 3 x - 7 | > - 6$