An inequality is defined as the expression that does not have equality sign joining the terms, but has the less than or greater than signs combining them. The objective of solving inequality is to find all the possible solutions of variables.

Several examples of inequality expressions are given below:

a – 2 > 5 or

3 s – 7 < 18 or

2 (p – 1) > 3 (2 p + 3)

(a + 3) / 2 > = 2 / 3

There are some rules that have to be followed to solve an inequality. These are as follows:

Rule no (1): When operations such as addition or subtraction are done, then add / subtract the terms from both the sides of the expression.

We can explain it by an example:

a – 2 > 5

Then to solve inequality add the number 2 on both sides.

a – 2 + 2 > 5 + 2

Or a > 7 is the solution.

Rule no (2): Inverse the operation when switching sides.

The above rule can be explained by an example as:

5 – p > 4 is an inequality then if we want to move left side term ( 5 – p) to right side and right side term 4 to the left side then sign of inequality '>' is changed to '<' as 4 < 5 – p .

Rule no (3): When there is an Operation of Multiplication or division then the operation will be done on both sides of inequality with the same number.

Or if there is an operation of multiplication or division with negative/positive number then also operations will be done on both sides of inequality with the same negative/positive number.

The above rule can be understood by an example: 2 a < + 6 are given inequalities then to solve inequality according to the above rule divide both sides by 2.

2 a / 2 <= + 6 / 2

a < = + 3.

We take some examples that define all the rules to solve the inequalities:

Solve inequality 2 a + 5 < 7

First subtract the number 5 from both sides:

2 a + 5 – 5 < 7 – 5

2 a < 2

Then divide the both sides of inequality as

2 a / 2 < 2 / 2

a < 1 .

Thus the solutions of inequality are all the Numbers less than one.

Solve inequality 5 – p < = 6

Subtract the number 5 from both sides

(5 – p) - 5 < = 6 – 5

-p < = 1

For removing the negative sign and also change < = to = > we multiply – p with – 1 on both side as -p * - 1 = > 1 * - 1

p = > - 1.

**Absolute values in inequalities must not be left unnoticed in mathematical solutions. They may seem a bit tough to be handled; still their importance holds in the inequality.**

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A linear equation is defined as an expression which includes a Combination of variables and constants and the degree of terms is one. Since an equation is represented by an equals to symbol according to which left hand side of the symbol must be equal to right hand side of the symbol. Similarly, an inequality is defined by two different symbols tha...Read More

Solving Inequalities Using Addition and Subtraction is quite interesting and important topic. Properties of inequalities are shown below:

Addition property of inequalities: for any number a, b, c

1: if a < b then a + c < b + c for example if 2, 3, 7 are three number where 2 < 3 then 2 + 7= 9 < 3 + 7 =10.

2: if a > b then a + c ...Read More

When two values are not equal to each other then we say that there is an inequality in both the values. Now we see the conditions of an inequality which are:

Suppose we have two variables ‘x’ and ‘y’;

If x ≠ y; which represents x is not equal to ‘y’;

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If we have two values and both the given values are not equal then we say that there is an inequality in both the values. Some of the conditions of an inequality are:

Suppose we have two variables ‘p’ and ‘q’;

If p ≠ q; which represents p is not equal to q;

And if p < q then we say that p is less than q;

And if p > q then we say tha...Read More