Solve the compound or absolute value inequality.
-$|6 x-4|

Question

Solve the compound or absolute value inequality.
-$|6 x-4|<9$

A) $\left(-\frac{5}{6}, \frac{13}{6}\right)$

B) $\left(-\infty,-\frac{5}{6}\right)$

C) $\left(-\infty,-\frac{5}{6}\right) \cup\left(\frac{13}{6}, \infty\right)$

D) $\varnothing$

Quizplus · Accepted Answer

To solve the inequality $|6x - 4| < 9$, we remove the absolute value by setting up two inequalities: $6x - 4 < 9$ and $6x - 4 > -9$. Solving the first gives $6x < 13$, so $x < \frac{13}{6}$, and solving the second gives $6x > -5$, so $x > -\frac{5}{6}$. Combining these gives the solution $\left(-\frac{5}{6}, \frac{13}{6}\right)$.

Solve the Compound or Absolute Value Inequality ∣6x−4∣<9|6 x-4|<9∣6x−4∣<9 A) (−56,136)\left(-\frac{5}{6}, \frac{13}{6}\right)(−65​,613​)

Solve the Compound or Absolute Value Inequality $|6 x-4|<9$ A) $\left(-\frac{5}{6}, \frac{13}{6}\right)$