# HOW TO FIND THE SOLUTION OF EACH INEQUALITY WITH GIVEN REPLACEMENT SET

## About "How to find the solution of each inequality with given replacement set"

How to find the solution of each inequality with given replacement set :

To find the solution for given inequality from given replacement set, we have to apply the values one by one from the given sets.

The values which satisfy the given inequality from the replacement set is the solution

## How to find solution of inequality from replacement set ?

• Apply each given values from the replacement set one by one.
• If the chosen value satisfy the given inequality, then we can decide that the particular value is the solution.
• Otherwise it is not the solution.

## Solution of an Inequality with Given Replacement Set - Examples

Example 1 :

Find the solution set for each inequality using the given replacement set.

a - 2 < 6; {6, 7, 8, 9, 10, 11}

Solution :

 a  =  66 - 2 < 64 < 6 (true) a  =  77 - 2 < 65 < 6 (true) a  =  88 - 2 < 66 < 6 (False)

From the given replacement set 6 and 7 are solutions.

Example 2 :

Find the solution set for each inequality using the given replacement set.

a + 7 < 22; {13, 14, 15, 16, 17}

Solution :

 a  =  13a + 7 < 2213 + 7 < 2220 < 22 (True) a  =  14a + 7 < 2214 + 7 < 2221 < 22 (True) a  =  15a + 7 < 2215 + 7 < 2222 < 22

Since, the values 13 and 14 are satisfying the given inequality. Those are the solutions.

Example 3 :

Find the solution set for each inequality using the given replacement set.

a/2 ≥ 5 ; {5, 10, 15, 20, 25}

Solution :

 a  =  5a/2 ≥ 55/2 ≥ 52.5 ≥ 5 (False) a  =  10a/2 ≥ 510/2 ≥ 55 ≥ 5 (True) a  =  15a/2 ≥ 515/2 ≥ 57.5 ≥ 5 (True)

10 is the first value which makes the given inequality true. For 15 also it becomes true. So we can decide that for all the numbers which are greater than 15 are also true.

Hence, 10, 15, 20, 25 are solution of the given inequality.

Example 4 :

Find the solution set for each inequality using the given replacement set.

2a/4 ≤ 8; {12, 14, 16, 18, 20, 22}

Solution :

 a  =  122a/4 ≤ 82(12)/4 ≤ 86 ≤ 8 (true) a  =  142a/4 ≤ 82(14)/4 ≤ 87 ≤ 8 (true) a  =  162a/4 ≤ 82(16)/4 ≤ 88 ≤ 8 (true)

a  =  18

2a/4 ≤ 8

2(18)/4 ≤ 8

9 ≤ 8 (False)

From the replacement set, 16 is the last value which satisfy the given inequality. For 18 it becomes false. So the values which are greater than 18 it will become false.

Hence 12, 14 and 16 are the solutions of the given inequality. After having gone through the stuff given above, we hope that the students would have understood "How to find the solution of each inequality with given replacement set".

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