# Absolute Value 1

### From Homeworkwiki

**Problem 1:Determine x when |x – 1| = 5**

**Solution:** When x – 1 is positive |x – 1| = x – 1

Therefore, x – 1 = 5; Implies, x = 6

When x – 1 is negative |x - 1| = -(x - 1) [Since, |x| = -x when x is negative]

Hence, the equation becomes –(x - 1) = 5

Therefore, x – 1 = -5

Implies, x = -5 +1 = -4

**Problem 2: Prove that |a| ^{2} = a^{2} **

**Solution:** If a is positive or 0, |a| = a

Therefore, |a|^{2} = a^{2}

If a is negative |a| = -a

Therefore, |a|^{2} = ( -a) ^{2} = a^{2}

In both the cases, squaring we get |a|^{2} = a^{2}