1. 2.5 Solving Compound Inequalities

2. Conjunctions- use the word “and”
x > 5 and x < 10
for the solution to x both statements must be true
a sentence like this means that x has to be larger than 5, but has to be 10 or less
Remember the line and closed points represent all possible solutions.
The graph…

3. More Examples x > -2 and x < 1
x has to be -2 or greater, but less than 1
-3 < x < 6
This is an abbreviated form of saying x has to be greater than -3, but less than 6

4. Try this…
a.) -3 < x and x < 4
b.) -7 < x < -3

5. Solve and Graph -6 < 2x + 4 < 10
-10 < 2x < 6
-5 < x < 3

6. Graph the conjunction.
-5 < x < 3

7. Try this… c.) -18 < 3x – 6 < -3 -18 < 3x – 6 < -3 +6 +6 +6
-12 < 3x < 3
-4 < x < 1

8. Disjunctions- use the word “or”
x < -3 or x > 6
One or both statements must be true
The graph…

9. Solve and graph -3x – 4 > 8 or x – 6 > 1
-3x > 12
x < -4
x – 6 > 1
+6 +6
x > 7

10. Try this…
d.) -2x – 6 > 4 or x + 5 > 8
x < -5 or x > 3