Find the solution set for the inequality.
- $5 + \left| \frac { 2 - x } { 2 } \right| < 8$

Question

Find the solution set for the inequality.
-$5 + \left| \frac { 2 - x } { 2 } \right| < 8$
A) $\{ x \mid x < - 4 \text { or } x > 8 \}$
B) $\{ x \mid - 4 < x < 8 \}$
C) $\{ x \mid - 4 < x < 4 \}$
D) $\{ x \mid - 8 < x < 4 \}$

Quizplus · Accepted Answer

To solve the inequality $5 + \left| \frac { 2 - x } { 2 } \right| < 8$, subtract 5 from both sides to get $\left| \frac { 2 - x } { 2 } \right| < 3$. This implies $-3 < \frac { 2 - x } { 2 } < 3$. Multiplying all parts by 2 gives $-6 < 2 - x < 6$. Solving the inequalities gives $x < 8$ and $x > -4$, which combined gives $-4 < x < 8$.

Find the Solution Set for the Inequality 5+∣2−x2∣<85 + \left| \frac { 2 - x } { 2 } \right| < 85+​22−x​​<8

Find the Solution Set for the Inequality $5 + \left| \frac { 2 - x } { 2 } \right| < 8$