1. First, add 5 to both sides of the equation:
|x| = 3 + 5
This simplifies to |x| = 8
2. Now, we have an absolute value equation. Recall that the absolute value of a number is its distance from zero on the number line. So, \(|x|\) is equal to either \(x\) or \(-x\), depending on whether \(x\) is positive or negative.
3. We can split the equation into two cases:
Case 1: If \(x \geq 0\), then \(|x| = x\).
Case 2: If \(x < 0\), then \(|x| = -x\).
4. For Case 1, substitute \(x\) for \(|x|\) in the equation:
\(x = 8\)
5. For Case 2, substitute \(-x\) for \(|x|\) in the equation:
\(-x = 8\)
6. Solve each equation separately:
Case 1: \(x = 8\)
Case 2: \(-x = 8\)
For Case 2, multiply both sides by \(-1\) to solve for \(x\):
\(x = -8\)
So, the solutions to the equation \(|x| - 5 = 3\) are \(x = 8\) and \(x = -8\).
