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Addition Property of Equality and Inequality

Definition of Addition Property of Equality and Inequality

Addition Property of Equality:
If the same number is added to both sides of an equation, the two sides remain equal.
That is, if x = y, then x + z = y + z.
Addition Property of Inequality:
Adding the same number to both sides of an inequality does not affect the inequality.
That is, if x > y, then x + z > y + z, and if x < y,="" then="" x="" +="" z="">< y="" +="" z.="">

Examples of Addition Property of Equality and Inequality

  • Addition Property of Equality
  • a) 3 = 3
  • Add the same number to both sides.
  • 3 + 2 = 3 + 2. It's true.
  • Addition Property of Inequality:
  • Adding the same number to both sides of an inequality does not affect the inequality. That is
  • if x > y, then x + z > y + z, and
  • if x < y,="" then="" x="" +="" z="">< y="" +="">

Video Examples: Addition property of equality and inequality


Solved Example on Addition Property of Equality and Inequality

Solve for X : x - 5 = 12

Choices:
  • A. 7
  • B. 17
  • C. - 7
  • D. 2.4

Correct Answer: B

Solution:

  • Step 1: x - 5 = 12
  • Step 2: x - 5 + 5 = 12 + 5
  • Step 3: x = 17

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