# Compound Inequality

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Compound inequality involves solving equation with two or more inequalities.  A sentence which says that one thing is not equal to another is called an inequality. Symbols of inequality are #,>, <,>=<=.  .Two or more inequality joined together to form compound inequality.  The relation of inequality between two integers remains the same even if equal integers are added to them or equal integers are subtracted from them. They are also multiplied by equal positive integers, or they are divided by equal positive integers.  The relation of inequality between two integers is inverted when they are multiplied or divided by negative integers.

The below mentioned two examples will help us in understanding the solving of inequality in better way.

Example 1:- Solve the inequality -2x – 5 < 15 for x.

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

=> -2x – 5 < 15

=> To cancel -5 add 5 on both sides

=> -2x -5 + 5 < 15 + 5

=> -2x < 20

=> Divide by -2 on both sides.

=> -2x / -2 < -20

=> The inequality symbol is inverted since they are divided by negative number.

=> X > -10. Hence solved.

Example 2:- Solve the inequality -50 < 7x+6 < -8

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

=> -50 < 7x+6 < -8

=> -50 - 6 < 7x + 6-6 < -8 -6                     (subtracting 6)

=> -56   < 7x < -14

=> Dividing by +7, so inequality is not inverted

=> -56/7 < 7x/7 < -14/7

=> -8 < x < -2

=> The value of x lies between -8 and -2.