An inequality expresses left-right ordering on a number line. Multiplication or division by a negative number causes a reflection about the origin of locations on a number line. When two different spots on the number line are reflected about the origin, their left-right order changes. Example -2 < 1 2 > -1 Both sides of an equation refer to the same spot on the number line. When reflected about the origin, they still refer to the same spot. Example 1 = 1 -1 = -1 Addition or subtraction shifts points right or left on the number line, so does not change the left-right ordering. Examples -2 < 1 -2 + 3 < 1 + 3, or 1 < 4 -1 = -1 -1 + 3 = -1 + 3, or 2 = 2
