Algebra I Chapter 3 Section 6: Quarter 2 Handout #2
Name _____________________ Date ________________ Period _____
Section 3.6: Compound Inequalities Rational & Special Cases
*Please refer to these general notes as we go over notes / practice problems in class AND while completing your homework!
We know that when we graph “and” inequalities we usually get a
shaded “dumbbell” and when we graph “or” inequalities we usually get
shaded “opposite arrows.”
BUT WHY???
And do we always get these results?
Let’s explore!
Algebra I Chapter 3 Section 6: Quarter 2 Handout #2

When graphing two inequalities at once what you are really doing is graphing each separately and then
o Look for the overlapping portion of the graphs for “and” statements (open circles take precedence since
must be included in both to be included at all!)

Ex. Graph x ≤ 9 AND x > -1 on a number line, then write the solution in interval notation

Ex. Graph m ≥ 2 AND m > 5 on a number line, then write the solution in interval notation
(Hint: you will get a shaded arrow!)
Algebra I Chapter 3 Section 6: Quarter 2 Handout #2
o Consider ALL values present for “or” statements (closed circles take precedence since only have
to be considered once to count!)

Ex. Graph y < -3 OR y ≥ 1, then write your solution in interval notation

Ex. Graph h > 1 OR h ≥ 3, then write your solution in interval notation (Hint: for this one your final
answer will only have one arrow shaded!)
Algebra I Chapter 3 Section 6: Quarter 2 Handout #2

SPECIAL CASES (ALL SOLUTIONS OR NO SOLUTION)
o AND  Sometimes there is no overlap between the individually graphed inequalities so nothing gets
shaded on the final number line; this is a case of “no solution”

Ex. Graph j > 1 AND j < -1
o OR  Sometimes when the two individually graphed inequalities are put together they cover, or span, the
entire number line; this is the case of “all solutions”

Ex. Graph w ≤ 2 OR w > -3, then write your solution in interval notation