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 <>, then x + z < y="" +="">.

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
    a) 2 <>
    Add the same number to both sides.
    2 + 1 < 3="" +="">
    i.e. 3 < 4.="" it’s="" true.="">

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

Related Terms for Addition Property of Equality and Inequality

  • Equality
  • Inequality
  • Equation