# Compound Inequalities

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Compound Inequalities are an effective tool for solving linear and quadratic in equations. Two or more inequality joined together to form compound inequality. The inequalities are joined with ‘and’   ‘or”. It can also be represented by single inequality. ‘And ‘represent intersection of inequalities and ‘Or’ represents union of inequalities. There are various methods for solving inequalities. We can use number line to represent inequalities.  Compound inequalities are mostly used in real world problems to find out the range. Addition - Subtraction rule and Multiplication-Division rules are to be followed while solving linear inequalities.

The below mentioned two examples will help us in understanding the same in better way.

Example 1:- Solve for x: -1 < 9 + n < 17. Then graph the solution.

Solution:- The steps to solve this equation are as follows:
-1 < 9 + n < 17

-1 – 9 < 9 + n – 9 < 17 – 9                     (use property)

- 10 < n < 8

The value of n lies between -10 and 8.

Representation by graph,

Example 2:- Solve the compound inequality 8x < 4 or 2x – 3 > 7. Then graph the solution.

Solution:- The steps to solve this equation are as follows:

4x < 8 or 2x – 3 > 7

Split the inequality as 4x < 8       or  2x – 3 > 7

Take first inequality

4x < 8

x < 2

Now take second inequality

2x – 3 > 7

2x > 10

x > 5

Therefore, we get x < 2 or x > 5.

By Graph,

These above examples help to understand the way to solve the compound inequalities and representing in

graph.