Solve the absolute value equation |5 - x| = 5.

Step-by-step solution

1. 1

   Read the inside expression carefully. The quantity inside the bars is $5-x$, not $x-5$. Since $|5-x|=|x-5|$ you could flip it, but there is no need — the two-case method works with either form as long as you keep the signs straight.

2. 2

   Write the two cases. Because the right-hand side $5$ is positive:

   $5-x=5\qquad\text{or}\qquad 5-x=-5$

3. 3

   Solve the first case. Subtracting $5$ from both sides leaves $-x=0$, hence

   $x=0$

4. 4

   Solve the second case. Subtract $5$ to get $-x=-10$, then multiply by $-1$:

   $x=10$

5. 5

   Verify and note the symmetry. $|5-0|=5$ $\checkmark$ and $|5-10|=|-5|=5$ $\checkmark$. Both answers lie $5$ units from $x=5$, the point where the inside vanishes — every equation $|x-a|=c$ has solutions $a\pm c$, which here reads $5\pm 5$.