Solve the inequality.Express the solution set in interval notation. $0

Question

Solve the inequality.Express the solution set in interval notation. $0 < | 4 x + 7 | < 11$
A) $\quad \left( - \frac { 7 } { 4 } , 1 \right)$
B) $\quad \left( - \infty , - \frac { 7 } { 4 } \right) \cup ( 1 , \infty )$
C) $\quad \left( - \frac { 9 } { 2 } , - \frac { 7 } { 4 } \right)$
D) $\quad ( - \infty , - 1 ) \cup \left( \frac { 7 } { 4 } , \infty \right)$
E) $\left( - \frac { 9 } { 2 } , - \frac { 7 } { 4 } \right) \cup \left( - \frac { 7 } { 4 } , 1 \right)$

Quizplus · Accepted Answer

First, we'll solve the inequality inside the absolute value:
$$0 < |4x+7| <11$$
Notice that we can split this into two separate inequalities:
$$0 < 4x+7 <11 \qquad 	ext{and} \qquad 0 < -(4x+7) < 11$$
Solving them separately gives:
$$-1.75 < x < 1 \qquad 	ext{and} \qquad -2 < x < -1.75$$
Combining these intervals gives:
$$\left(-\frac{9}{2}, -\frac{7}{4}ight) \cup \left(-\frac{7}{4}, 1ight)$$
Therefore, the answer is E.

Solve the Inequality 0<∣4x+7∣<110 < | 4 x + 7 | < 110<∣4x+7∣<11

Solve the Inequality $0 < | 4 x + 7 | < 11$