Solve the inequality algebraically. Write the solution in interval notation.
-$$| 4 x + 3 |

Question

Solve the inequality algebraically. Write the solution in interval notation.
-$$| 4 x + 3 | < 6$$
A) $( - \infty , 4 )$
B) $\left( - \infty , - \frac { 9 } { 4 } \right) \cup \left( \frac { 3 } { 4 } , \infty \right)$
C) $\left( - \frac { 9 } { 4 } , \frac { 3 } { 4 } \right)$
D) $\left( - \infty , - \frac { 9 } { 4 } \right)$

Quizplus · Accepted Answer

To solve the inequality $| 4x + 3 | < 6$, we consider two cases: $4x + 3 < 6$ and $4x + 3 > -6$. Solving these gives $x < \frac{3}{4}$ and $x > -\frac{9}{4}$, respectively. Combining these gives the solution $\left( - \frac { 9 } { 4 } , \frac { 3 } { 4 } \right)$.

Solve the Inequality Algebraically ∣4x+3∣<6| 4 x + 3 | < 6∣4x+3∣<6

Solve the Inequality Algebraically $| 4 x + 3 | < 6$