# COMPOUND INEQUALITIES AND OR

## About "Compound inequalities and or"

Compound inequalities and or :

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.

That is, we have to shade the portion that we find in both graphs. If the particular region is not in one of the graphs, we should not shade the region.

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.

 and - Intersection Or-Union

## Compound inequalities and or Examples

Example 1 :

Solve each compound inequality. Then graph the solution set.

h - 10 < - 21  (or)  h + 3 < 2

Solution :

h - 10 < - 21  (or)  h + 3 < 2

 h - 10 < - 21Add 10 on both sidesh - 10 + 10 < -21 + 10h  < -11 h + 3 < 2Subtract 3 on both sidesh + 3 - 3 < 2 - 3h < -1

Now let us graph for the first inequality

h < -11

We have to shade the portion, which is lesser than -11. Since it is less than sign, we have to use the unfilled circle

Now let us graph for the second inequality

h < -1

We have to shade the portion, which is lesser than -1. Since it is less than sign, we have to use the unfilled circle

By combining the above two graphs, we get

Example 2 :

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.

After having gone through the stuff given above, we hope that the students would have understood "Compound inequalities and or".

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