Solve the inequality and give the solution set.
-$- 4

Question

Solve the inequality and give the solution set.
-$- 4 < \frac { - 3 ( 4 - x ) } { 5 } < \frac { 2 } { 9 }$
A) $\left\{ x \mid - \frac { 8 } { 3 } < x < \frac { 22 } { 3 } \right\}$
B) $\left\{ x \mid - \frac { 118 } { 27 } < x < \frac { 8 } { 3 } \right\}$
C) $\left\{ x \mid - \frac { 22 } { 3 } < x < \frac { 8 } { 3 } \right\}$
D) $\left\{ x \mid - \frac { 8 } { 3 } < x < \frac { 118 } { 27 } \right\}$

Quizplus · Accepted Answer

To solve the inequality $- 4 < \frac { - 3 ( 4 - x ) } { 5 } < \frac { 2 } { 9 }$, first multiply all parts by 5 to get rid of the denominator: $-20 < -3(4-x) < \frac{10}{9}$. Then distribute the -3: $-20 < -12 + 3x < \frac{10}{9}$. Add 12 to all parts: $-8 < 3x < \frac{118}{9}$. Finally, divide by 3 to solve for x: $-\frac{8}{3} < x < \frac{118}{27}$.

Solve the Inequality and Give the Solution Set −4<−3(4−x)5<29- 4 < \frac { - 3 ( 4 - x ) } { 5 } < \frac { 2 } { 9 }−4<5−3(4−x)​<92​

Solve the Inequality and Give the Solution Set $- 4 < \frac { - 3 ( 4 - x ) } { 5 } < \frac { 2 } { 9 }$