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High School Mathematics - 2
7.1 Inequality Postulates

1. Adding to or subtracting from both sides of an inequality and non-zero number produces an equivalent inequality
  1. x-3 > 5 is equivalent to x-3+3 > 5+3 or x > 5+3 or x > 8
  2. x+1 > 3 is equivalent to x+1-1 > 3-1, x > 3-1 or x > 2
2. Multiplying or dividing both sides of an inequality by the same positive number produces an equivalent inequality.
  1. 5x > 15 is equivalent to 5x/15 > 15/5, or x > 15/5 or x > 3
  2. x/3 > 2 is equivalent to x/3.3 > 2.3, or x > 2.3 or x > 6
Multiplying both sides of an inequality by the same negative number produces an inequality with its direction reversed.

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