Find x if |11 - 12| = x.

Step-by-step solution

1. 1

   Spot where the unknown lives. Here $x$ is outside the absolute value bars, so there is no equation to case-split — the left side is a fixed number and the task is simply to compute it.

2. 2

   Work inside the bars first. Absolute value acts like a grouping symbol, so the subtraction happens before the bars are applied:

   $11-12=-1$

3. 3

   Apply the absolute value. The distance from $-1$ to $0$ is $1$:

   $|-1|=1$

   So $x=1$.

4. 4

   Sanity-check with the order-independence rule. $|a-b|=|b-a|$, so computing $12-11=1$ and then $|1|=1$ gives the same answer. That is a handy check: the order of subtraction inside absolute value bars never changes the result.