Solve the inequality.Express the solution set in interval notation. $$8

Question

Solve the inequality.Express the solution set in interval notation. $$8 < \left| \frac { x - 23 } { 3 } \right| < 10$$
A) $\quad ( - 7 , - 1 ) \cup ( 47,53 )$
B) $( - 53 , - 47 ) \cup ( 1,7 )$
C) $\quad ( - 1,47 )$
D) none of the above
E) $( - 7,1 ) \cup ( 47,53 )$

Quizplus · Accepted Answer

To solve the inequality $8 < \left| \frac { x - 23 } { 3 } \right| < 10$, we break it into two parts: $8 < \left| \frac { x - 23 } { 3 } \right|$ and $\left| \frac { x - 23 } { 3 } \right| < 10$. For the first part, we have two cases: $\frac { x - 23 } { 3 } > 8$ and $\frac { x - 23 } { 3 } < -8$. Solving these gives $x > 47$ and $x < -1$, respectively. For the second part, we also have two cases: $\frac { x - 23 } { 3 } < 10$ and $\frac { x - 23 } { 3 } > -10$. Solving these gives $x < 53$ and $x > -7$, respectively. Combining these results, we get the solution set $( - 7 , - 1 ) \cup ( 47,53 )$.

Solve the Inequality 8<∣x−233∣<108 < \left| \frac { x - 23 } { 3 } \right| < 108<​3x−23​​<10

Solve the Inequality $8 < \left| \frac { x - 23 } { 3 } \right| < 10$