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

Question

Solve the inequality. Express the solution set in interval notation.
$$0 < | 4 x + 3 | < 7$$
A) $\quad \left( - \frac { 5 } { 2 } , - \frac { 3 } { 4 } \right)$
B) $\left( - \frac { 5 } { 2 } , - \frac { 3 } { 4 } \right) \cup \left( - \frac { 3 } { 4 } , 1 \right)$
C) $\left( - \frac { 3 } { 4 } , 1 \right)$
D) $\left( - \infty , - \frac { 3 } { 4 } \right) \cup ( 1 , \infty )$
E) $( - \infty , - 1 ) \cup \left( \frac { 3 } { 4 } , \infty \right)$

Quizplus · Accepted Answer

First, we can split the inequality into two parts, one for $4x+3>0$ and one for $4x+3<0$. For $4x+3>0$, we have $|4x+3|=4x+3$, so $0<4x+3<7$ Solving this inequality gives $-\frac{3}{4}

Solve the Inequality 0<∣4x+3∣<70 < | 4 x + 3 | < 70<∣4x+3∣<7

Solve the Inequality $0 < | 4 x + 3 | < 7$