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Compound Compound InequalitiesInequalitiesCompound Compound InequalitiesInequalities
““And” & “Or”And” & “Or”Graphing SolutionsGraphing Solutions
Compound Inequality ---Two or more inequalities that are connected by the words “and” or “or”.
This inequality is true only if both inequalities are true. The solution must be a solution for both inequalities! We will graph where the two inequalities intersect.
This inequality is true if one or the other inequality is true. The solution is a solution of either inequality. We will graph the union— graph both inequalities.
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-3 -2 -1 0 1 2 3 4 5
1. Graph the solution set of x < 3 x ≥ -2
<---|---|---|---|---|---|---|---|---|--->
-3 -2 -1 0 1 2 3 4 5
<---|---|---|---|---|---|---|---|---|--->
-3 -2 -1 0 1 2 3 4 5
Graph x < 3
Graph x ≥ -Graph x ≥ -22
Find the intersection
2 3x
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
2. Graph the solution set of x ≤ 8 x > -6
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
Graph x ≤ 8
Graph x > -Graph x > -66
Find the intersection
6 8x
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
3. Graph the solution set of x > -2 x > 1
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
Graph x > -2
Graph x > Graph x > 11
Find the intersection
1x
4. Solve and Graph the solution set of
5 4 2x 44 4
6
1 6x <---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
1 x
5. Solve and Graph the solution set of
9 2 1 3x 11 1
4
4 2x
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
8 2x 2 2 2
6. Solve and Graph the solution set of
2 3 11 3 7 8x x 3 3
2 8 x 2 2
4 x
7 73 15 x
3 3 x 5
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10Where
Do theyIntersect? <---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
7. Solve and Graph the solution set of
2 3 1 3 3 12x x 3 3
2 2 x 2 2
1x
3 33 9 x
3 3 x 3
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10Where
Do theyIntersect? <---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
Doesn’tCross…
SoNO
Solution!
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
8. Graph the solution set of x ≤ 0 x > 6
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
Graph x ≤ 0
Graph x > Graph x > 66
Find the Union
Just graphBoth
Inequalities!
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
9. Graph the solution set of x > -4 x > 6
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
Graph x > -4
Graph x > Graph x > 66
Find the Union
Just graphBoth
Inequalities!
The first one containsAll the points in the2nd inequality…so
x > -4 is the answer.
10. Solve and Graph the solution set of
2 5 1 4 3 11x x 5 5
2 4 x 2 2
2x
3 34 8 x
4 4 x 2
<---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10Graph Both
Inequalities <---|---|---|---|---|---|---|---|---|--->
-6 -4 -2 0 2 4 6 8 10
x < -2 is included in
x < 2
