Solve each equation.
1. $|x|=8$

Step 1 ：The equation is $|x|=8$.

Step 2 ：The absolute value of a number is its distance from zero on the number line. Therefore, the absolute value of a number is always positive or zero, but never negative.

Step 3 ：The equation $|x|=8$ means that the distance of $x$ from zero on the number line is 8 units. This can happen in two cases:

Step 4 ：Case 1: $x$ is 8 units to the right of zero. In this case, $x=8$.

Step 5 ：Case 2: $x$ is 8 units to the left of zero. In this case, $x=-8$.

Step 6 ：So, the solutions to the equation $|x|=8$ are $x=8$ and $x=-8$.

Step 7 ：To check these solutions, we can substitute them back into the original equation:

Step 8 ：If $x=8$, then $|8|=8$, which is true.

Step 9 ：If $x=-8$, then $|-8|=8$, which is also true.

Step 10 ：Therefore, the solutions $x=8$ and $x=-8$ are correct.

Step 11 ：So, the final answer is $\boxed{{\displaystyle x=8}}$ and $\boxed{{\displaystyle x=-8}}$.