Absolute Values

Aboslute Laws:

The absolute value of a no. x = (lxl) can be thought of as being the distance which the no. x is from 0 on the number line.
Therefore lxl = x or -x.
NOTE. Distance is always positive or 0

1. lxl > or = 0

2. lxl = root x²

3. lx + yl < or = lxl + lyl (triangel equality i.e equality holds when x > or = 0 and y > or = 0)

4. lx - yl < or = lxl - lyl (equality holds when x > or = 0 and y > or = 0)

5. lxyl = lxl lyl

6. lx / yl = lxl / lyl

7. lx²l = lxl²

Absolute Values:

1. if lxl = a

x = a or x = -a

For example: if lxl = 3
x = 3 or -3

2. if lx + ml = a
x + m = a or x + m = -a

3. The lxl = l-xl

For example: l-3l = l3l

4. lx - al = la - xl

For example: lx - 5l = l5 - xl

5. alxl = laxl only if a > or = 0

For example: 2l-3l = 2 x 3 = 6
l2 x 3l = 6

but -3l4l = -12
l-3 x 4l = 12

By Muhammed, Wesley and Chao