lesson 3-5 objectives the student will be able to: 1. solve compound inequalities. 2.graph the...
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Lesson 3-5Objectives
The student will be able to:
1. solve compound inequalities.
2. graph the solution sets of compound inequalities.
Designed by Skip Tyler, Varina High School
--A compound inequality is when you SMUSH two inequalities together. --There are two types of compound inequalities:
1. AND - TODAY
2. OR - TOMORROW
Designed by Skip Tyler, Varina High School
What is the difference between and and or?
AND means intersection-what the two items have
in common
OR means union-some answers are in one
circle, some answers are in the other…none in the middle
A B
A B
Let’s look at some AND problems…intersection!
A B
1) Graph x < 4 and x ≥ 2
3 42●
a) Graph x < 4
b) Graph x ≥ 23 42
o
c) Combine the graphs
●
3 42o
d) Where do they intersect?●
3 42o
2) Which inequalities describe the following graph?
-2 -1-3oo
Answer NowAnswer Now
1. y > -3 or y < -1
2. y > -3 and y < -1
3. y ≤ -3 or y ≥ -1
4. y ≥ -3 and y ≤ -1
When written this way, it is the same thing as
6 < m AND m < 8
It can be rewritten as
m > 6 and m < 8
and graphed as previously shown, however,
it is easier to graph everything
between 6 and 8!
3) Graph the compound inequality 6 < m < 8
7 86oo
4) Which is equivalent to-3 < y < 5?
1. y > -3 or y < 5
2. y > -3 and y < 5
3. y < -3 or y > 5
4. y < -3 and y > 5
Answer NowAnswer Now
5) Which is equivalent to x > -5 and x ≤ 1?
1. -5 < x ≤ 1
2. -5 > x ≥ 1
3. -5 > x ≤ 1
4. -5 < x ≥ 1
Answer NowAnswer Now
6) Graph 3 < 2m – 1 < 9
0 5-5
+ 1 +1 +1
4 < 2m < 10 /2 /2 /2
2 < m < 5
7) Graph -16 < -3x + 8 < -7
Remember, it can also look like this sometimes!
-16 < -3x + 8 AND -3x + 8 < -7
0 85
-8 -8 -8
-24 < -3x < -15
8 > x > 5
/-3 /-3 /-3
FLIP THE SIGNS!!!
5 < x < 8
8) 2x < -6 and 3x ≥ 12
1. Solve each inequality for x
2. Graph each inequality3. Combine the graphs4. Where do they
intersect?5. They do not! x cannot
be greater than or equal to 4 and less than -3 No Solution!!
2 6
2 2 3
x
x
3x 12
3 3 x 4
-3 0-6o-3 0-6o
4 71o●4 71o●
Now…let’s try some AND problems on your clickers!
Remember from yesterday…What is the difference between
and and or?AND means intersection
-what the two items have in common
OR means union-some answers are in one
circle, some answers are in the other…none in the middle
A B
A B
Let’s look at some OR problems…different directions!
A B
9) Graph x < 2 or x ≥ 4
3 42●
a) Graph x < 2
b) Graph x ≥ 43 42
o
c) Combine the graphs
3 42o
3 42●
10) Graph x < 2 or x ≥ 4
0 5-5
11) Graph x ≥ -1 or x ≤ 3
The whole line is shaded!! Weird, huh?!
0 5-5
11) Graph 2m – 1 < 3 or 2m – 1 > 9
Remember, solve each inequality as a separate problem then graph it on the same number line.
2m – 1 < 3 or 2m – 1 > 9
Graph the direction of m < 2 or m > 5.
0 5-5
12) Graph -3n < -9 or -2n > 10
Remember, solve each inequality as a separate problem then graph it on the same number line.
-3n < -9 or -2n > 10
Graph the direction of n < -5 or n > 3.
0 3-5
Let’s try some OR problems on the clickers!
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