Solve the equation or inequality.
-$| x - 3 | = | 8 - x |$
A) $\frac { 11 } { 2 }$
B) 11
C) $\varnothing$
D) $- \frac { 2 } { 11 }$

Question

Quizplus · Accepted Answer

The absolute value equation $| x - 3 | = | 8 - x |$ implies that the distance of $x$ from 3 is the same as its distance from 8 on the number line. To solve, we can set the expressions inside the absolute values equal to each other and also consider the case where they are negatives of each other. However, in this case, since both forms are symmetric, we only need to solve one equation: $x - 3 = 8 - x$. Solving for $x$, we get $2x = 11$, so $x = \frac{11}{2}$.

Solve the Equation or Inequality ∣x−3∣=∣8−x∣| x - 3 | = | 8 - x |∣x−3∣=∣8−x∣

Solve the Equation or Inequality $| x - 3 | = | 8 - x |$