Solve: $| - 5 + 9 x | - 12

Question

Solve: $| - 5 + 9 x | - 12 < 12$
A) $x < \frac { 29 } { 9 }$
B) $- \frac { 29 } { 9 } < x < \frac { 19 } { 9 }$
C) $- \frac { 19 } { 9 } < x < \frac { 29 } { 9 }$
D) $- \frac { 5 } { 9 } < x < - \frac { 5 } { 9 }$
E)no solution

Quizplus · Accepted Answer

First, we solve the inequality $| - 5 + 9 x | - 12 < 12$. Adding 12 to both sides gives $| - 5 + 9 x | < 24$. This means $-24 < -5 + 9x < 24$. Solving the left part, $-24 + 5 < 9x$, gives $x > -\frac{19}{9}$. Solving the right part, $-5 + 9x < 24$, gives $x < \frac{29}{9}$. Combining these gives $-\frac{19}{9} < x < \frac{29}{9}$.

Solve ∣−5+9x∣−12<12| - 5 + 9 x | - 12 < 12∣−5+9x∣−12<12

Solve $| - 5 + 9 x | - 12 < 12$