Solve the equation.
-$| x + 6 | = | 9 - x |$
A) $\left\{ \frac { 3 } { 2 } \right\}$
B) {3}
C) $\left\{ - \frac { 2 } { 3 } \right\}$
D) $\phi$

Question

Solve the equation.
-$| x + 6 | = | 9 - x |$
A) $\left\{ \frac { 3 } { 2 } \right\}$
B)  {3} 
C) $\left\{ - \frac { 2 } { 3 } \right\}$
D) $\phi$

Quizplus · Accepted Answer

The equation $| x + 6 | = | 9 - x |$ can be solved by considering two cases due to the absolute value: 1) $x + 6 = 9 - x$, which simplifies to $2x = 3$, giving $x = \frac{3}{2}$, and 2) $x + 6 = -(9 - x)$, which simplifies to $x + 6 = -9 + x$, leading to a contradiction, indicating no solution from this case. Thus, the only solution is $x = \frac{3}{2}$.

Solve the Equation ∣x+6∣=∣9−x∣| x + 6 | = | 9 - x |∣x+6∣=∣9−x∣

Solve the Equation $| x + 6 | = | 9 - x |$