# SOLVING COMPOUND INEQUALITIES EXAMPLES

## About "Solving compound inequalities examples"

Solving compound inequalities examples :

Here we are going to see some examples based on the concept solving compound inequalities.

A compound inequality is an equation with two or more inequalities joined together with either "and" or "or" (for example, x ≥ 6 and  x < 3 x < -12 or x ≥ 8).

Compound inequalities with "And" :

A compound inequality containing and is true only if both inequalities are true. Thus, the graph of a compound inequality containing and is the intersection of the graphs of the two inequalities.

In other words, the solution must be a solution of both inequalities.

The intersection can be found by graphing each inequality and then determining where the graphs overlap.

Compound inequalities with "Or" :

Another type of compound inequality contains the word or. A compound inequality containing or is true if one or more of the inequalities is true. The graph of a compound inequality containing or is the of the graphs of the two inequalities.

In other words, the solution of the compound inequality is a solution of either inequality, not necessarily both. The union can be found by graphing each inequality.

Example 1 :

Solve the compound inequality. Then graph the solution set

k + 2 > 12 and k + 2 ≤ 18

Solution :

 k + 2 > 12 Subtract by 2 on both sidesk + 2 - 2  > 12 - 2k > 10 k + 2 ≤ 18Subtract by 2 on both sidesk + 2 - 2  ≤ 18 - 2k ≤ 16

By graphing the inequality k > 10, we get the graph given below.

By graphing the inequality ≤ 16, we get the graph given below.

By combining the above two graphs, we get the common region between 10 and 16.

Example 2 :

Solve the following inequality and graph the solution

3 < 2x - 3 < 15

Solution :

3 < 2x - 3 < 15

3 + 3 < 2x – 3 + 3 < 15 + 3

6 < 2x < 18

Divide by 2

6/2 < 2x/2 < 18/2

3 < x < 9

Example 3 :

Solve the following inequality and graph the solution

3t – 7 ≥ 5 and 2t + 6 ≤  12

Solution :

3t – 7 ≥ 5 and 2t + 6 ≤  12

 3t – 7 ≥ 5Add 7 on both sides3t – 7 + 7 ≥ 5 + 73t  ≥ 12Divide by 3 on both sides 3t/3  ≥ 12/3t  ≥ 4 2t + 6 ≤  12Subtract 6 on both sides2t + 6 – 6 ≤  12 – 62t ≤  6Divide by 2 on both sidest ≤  3

t  ≥ 4 and t ≤  3

Example 4 :

Solve the following inequality and graph the solution

4m - 5 > 7 or 4m - 5 < -9

Solution :

 4m - 5 > 7Add 5 on both sides4m - 5 + 5 > 7 + 54m > 12Divide by 4 on both sides 4m/4  > 12/4m > 3 4m - 5 < -9Add 5 on both sides4m - 5 + 5 < -9 + 54m < -4Divide by 4 on both sides4m/4 < -4/4m < -1

After having gone through the stuff given above, we hope that the students would have understood "Solving compound inequalities examples".

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