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

Question

Solve the inequality algebraically. Write the solution in interval notation.
-$| 4 - 4 x | - 3 < 4$
A) $\left( - \frac { 3 } { 4 } , \infty \right)$
B) $\left( - \frac { 3 } { 4 } , \frac { 11 } { 4 } \right)$
C) $\left( - \infty , - \frac { 3 } { 4 } \right)$
D) $\left( - \infty , - \frac { 3 } { 4 } \right) \cup \left( \frac { 11 } { 4 } , \infty \right)$

Quizplus · Accepted Answer

To solve the inequality $| 4 - 4x | - 3 < 4$, first isolate the absolute value expression:$$| 4 - 4x | < 7$$This inequality splits into two cases:1. $4 - 4x < 7$2. $4 - 4x > -7$Solving each case:1. $4 - 4x < 7$ $-4x < 3$ $x > -\frac{3}{4}$2. $4 - 4x > -7$ $-4x > -11$ $x < \frac{11}{4}$Combining both inequalities gives the solution interval $\left( -\frac{3}{4}, \frac{11}{4} \right)$.

Solve the Inequality Algebraically ∣4−4x∣−3<4| 4 - 4 x | - 3 < 4∣4−4x∣−3<4

Solve the Inequality Algebraically $| 4 - 4 x | - 3 < 4$