# Inequalities in Mathematics

## Definition:

Inequalities represent relation of two algebraic expressions in which one expression is greater or less than other expression. For example x > 5, 4x + 5 < 20, x + y > 1

Solution of an inequality is a set of all values which satisfy the inequality. It is not a single value, for example x > 5 means that all numbers greater than 5 consist solution set.

Addition of subtraction of same number on both sides does not affect inequality. If both sides are multiplies or divided by same positive number (except ‘0’) inequality remains same. Both side can be squared. Square root can be taken if both the sides are positive. Multiplying or dividing both sides with a negative number reverses the inequality. Taking reciprocal of both sides reverses the inequality.

The methods which are used to solve equations can also be used to solve the inequalities. Following are some examples along with explanations which will clear the situation further:-

## Inequalities Examples

Example No.1

If 2x + 5y = 18 and x=4 then what is the value of y?

a) 2 b) 3 c) 4 d) 5

Explanation

**a) is answer**

By putting value of x in equation

2(4) + 5y = 18

5y = 18 – 8

Y = 10/5 = 2

Example No.2

In all Pakistan Weight Lifting competition in Multan, double of first lift of Mr. Sahiwal was 150 kilograms more than his second lift and the sum of two lifts was 375 kilograms.What was the weight of his first lift?

a) 300 b) 350 c) 175 d) 100

c) is answer

L is the weight of first lift and P is the weight of the second lift. Based on given condition you have the equation 2L=P+150 and L+P=375

Example No.3

Twice the age of son is 4 years more than the age of his father. What is the age of son if father is of 40?

a) 22 b) 20 c) 18 d) 16

a) is answer

Equation is bases on given condition that 2Son – 4 = Father, Now Father=40

2Son = 40 + 4, Son = 22