Solve.
-$| x - 6 | = | 2 - x |$
A) {8}
B) $\left\{ - \frac { 1 } { 4 } \right\}$
C) $\{ 4 \}$
D) $\phi$

Question

Solve.
-$| x - 6 | = | 2 - x |$
A)  {8} 
B) $\left\{ - \frac { 1 } { 4 } \right\}$
C) $\{ 4 \}$
D) $\phi$

Quizplus · Accepted Answer

The equation $| x - 6 | = | 2 - x |$ can be solved by considering two cases due to the absolute value:1. $x - 6 = 2 - x$, which simplifies to $2x = 8$, giving $x = 4$.2. $x - 6 = -(2 - x)$, which simplifies to $x - 6 = -2 + x$, leading to a contradiction since the $x$ terms cancel out, leaving $-6 = -2$, which is false.Therefore, the only solution is $x = 4$, which corresponds to choice C.

Solve - ∣x−6∣=∣2−x∣| x - 6 | = | 2 - x |∣x−6∣=∣2−x∣

Solve
- $| x - 6 | = | 2 - x |$