Solve.
-$| 4 x + 8 | = | x - 9 |$
A) $\left\{ - \frac { 17 } { 3 } , \frac { 1 } { 5 } \right\}$
B) $\left\{ \frac { 17 } { 3 } , - \frac { 1 } { 5 } \right\}$
C) $\left\{ - \frac { 17 } { 3 } , 5 \right\}$
D) $\phi$

Question

Quizplus · Accepted Answer

To solve $| 4x + 8 | = | x - 9 |$, we consider two cases due to the absolute value:1. $4x + 8 = x - 9$Solving for $x$, we subtract $x$ and add $9$ to both sides:$$3x = -17$$$$x = -\frac{17}{3}$$2. $4x + 8 = -(x - 9)$Expanding and solving for $x$, we get:$$4x + 8 = -x + 9$$$$5x = 1$$$$x = \frac{1}{5}$$Thus, the solution set is $\left\{ - \frac { 17 } { 3 } , \frac { 1 } { 5 } \right\}$.

Solve - ∣4x+8∣=∣x−9∣| 4 x + 8 | = | x - 9 |∣4x+8∣=∣x−9∣

Solve
- $| 4 x + 8 | = | x - 9 |$