Subtractive Property of Equations and Inequalities      

           Definitions of Subtractive Property of Equations and Inequalities

• Subtractive Property of Equations: If the same number is subtracted from both sides of an equation, then the two sides remain equal.

That is,  if x = y, then x - z = y - z.

• Subtractive Property of Inequalities: Subtracting the same number from 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 Subtractive Property of Equations and Inequalities

• Addition Property of Equality:

a) 3 = 3

Subtract the same number from both sides,

3 - 2 = 3 - 2, its true

• Addition Property of Inequality

  a) 2 < 3

  Subtract the same number from both sides,

  2 - 1 < 3 - 1

  < 2, its true

Solved Example on Subtractive Property of Equations and Inequalities

          If a + 15 = 10, then what is the value of a?

Choices:                     

A. - 5

B. - 15

C. 5

D. 15

Correct answer: A

Solution:  

Step 1: a + 15 = 10           [Given.]

Step 2: a + 15 – 15 = 10 - 15       [Subtract – 15 from both the sides.]

Step 3: a = - 5

           

Related Terms for Subtractive Property of Equations and Inequalities

• Equality
• Inequality
• Subtraction

 

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