Transcript 6.3 Solving Compound Inequalities

Algebra
6.3
Solving Compound Inequalities
The difference between the
words “and” and “or”
If your mother tells you to do something, do the words she uses
make a difference?
“Please take out the garbage and make your bed.”
“Please take out the garbage or make your bed.”
How many chores do you have if she uses the word “and”?
Two. You have to do both chores.
How many chores do you have if she uses the word “or”?
One. You only have to do one chore or the other.
Compound Inequality (2 types)
Two inequalities connected by and or or.
And
Or
Both inequalities must be true
-2 < x ≤ 3
means -2 < x and x ≤ 3
All real numbers greater than -2 and less than
or equal to 3.
Only one inequality must be true
x ≤ -4 or x > 2
All real numbers less than or equal to -4 or
greater than 2.
Graphs of Compound Inequalities
And
Look like this:
Or
Look like this:
Graphs of Compound Inequalities
And
-2 < x ≤ 3
means -2 < x and x ≤ 3
All real numbers greater than -2 and
less than or equal to 3.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
Graphs of Compound Inequalities
Or
x ≤ -4 or x > 2
All real numbers less than or equal to
-4 or greater than 2.
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5
Example
Solve:
-5 ≤ 2x +3 < 7
-3
-3
-3
-8 ≤ 2x
< 4
2
2
2
-4 ≤ x < 2
-5 -4 -3 -2 -1 0 1 2 3
Example
Solve:
-2 < -2 - x < 1
+2
+2
+2
0 <
-1
0
-3
>
<
-x
-1
x
x
< 3
-1
> -3
<
0
Rewrite in
number line order
-5 -4 -3 -2 -1 0 1 2 3
You try
Solve:
-5 ≤ -2x +3 < 9
-3
- 3 -3
-8 ≤ -2x
< 6
-2
-2
-2
4 ≥ x > -3
-3 < x ≤ 4 Number line order
-4 -3 -2 -1 0 1 2 3 4 5
Example
Solve:
6x – 5 < 7
or
8x + 6 ≥ 46
+5 +5
or
-6
6x < 12
or
6
6
x < 2 or
-6
8x ≥ 40
8
8
x≥5
-1 0 1 2 3 4 5 6 7
You try
Solve:
3x + 1 ≤ 4
or
2x - 5 > 7
-1 -1
or
+5 +5
3x ≤ 3
or
3
3
x ≤ 1 or
2x > 12
2
2
x>6
-1 0 1 2 3 4 5 6 7
A few together from the HW

P. 349 #18, #26, #32
Homework
Pg. 349 #18-35, 55-69