Addition Property of Inequality

 
Inequality is an expression having terms that does not equal. The inequality expressions having a symbols like < , >.
For example, 7 is less than 8 which is written as 7 < 8 or 8 > 7. Here the numbers 7 and 8 are inequalities. Addition property of inequality shows how the inequality expression is changed during addition operation.Addition Property of Inequality:
There are two properties for addition of inequality.

 

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Property 1:
The addition of a same number on both sides of inequality can not change the meaning of inequality.
Example:
Consider an inequality expression c > d.
Add a term ‘a’ on both sides. Then the inequality expression is
c + a > d + a
Same as the inequality expression c < d.
Addition of a term ‘a’ can not change the meaning.
c + a < d + a
Property 2:
Addition of different numbers on both sides also can not change the meaning of inequality. In this case, the number going to add at left side must be smaller than the number going to add at right.
Example:
Consider an inequality k < l.
k + p < l + q and p < q.Example Problems to Addition Property of Inequality:
Example: 1
What is the value of ‘x’ of an inequality expression x + 1 > 3.
Solution:
Given,
Inequality x + 1 > 3
For finding the value of x, consider it as equality.
That is , x + 1 = 3
X = 3 -1
X = 2
For x= 2 the expression is equality. For inequality the value of x should be greater than 2.
Answer: x = 3 and above.
Example: 2
What is the value of ‘x’ of an inequality expression x + 3 < 5.
Solution:
Given, x + 3 < 5.
Consider it as equality. x + 3 = 5
X = 5 -3
X = 2
For x = 2 the inequality becomes equality.
For x< 2 the expression of inequality it true.
Answer: x is less than 2.Practice Problems to Addition Property of Inequality:
Problem: 1
What is the value of x in inequality x + 8 > 10
Answer: 3 and above.

 

Problem: 2
What is the value of x in inequality x + 5 > 12
Answer: 8 and above.