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 \(\boxed{x=8}\) and \(\boxed{x=-8}\).