Why Does The Inequality Sign Change When Both Sides Are Multiplied Or Divided By A Negative Number? Does This Happen With Equations? Why Or Why Not? Write An Inequality And In The Inequality Use Both The Multiplication And Addition Properties Of Ine

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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

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