Date post: | 23-Dec-2015 |
Category: |
Documents |
Upload: | anastasia-booker |
View: | 213 times |
Download: | 0 times |
Unit 3 Day 5: Solving One and Two Step Linear
InequalitiesEssential Questions: How do we graph linear inequalities in one variable? How do we solve
one and two step linear inequalities?
Vocabulary
• Graph of the Inequality: the set of points on a number line that represent all solutions of the inequality.
Inequality Signs (as read from left to right )
All real numbers less than 2
All real numbers greater than -2
All real numbers less than or equal to 1
All real numbers greater than or equal to 0
x < 2
x > -2
x < 1
0 1 2 3-1-2
0 1 2 3-1-2
0 1 2 3-1-2
0 1 2 3-1-2
Graphing Linear Inequalities
x > 0
When graphing inequalities use an:• open dot for < and > • close dot for ≤ and ≥• Draw a ray in the direction of the inequality sign.
Verbal Phrase: Graph :
Example 1: Graph the inequality.
x > -7 x < 1
Sarah was sure that she scored at least a 73% on her algebra test. Write and graph an inequality for Sarah’s possible test scores.
-7 1
x ≥ -9
-9
x ≤ 10
10
s > 7373
Solving Linear InequalitiesWhen solving linear inequalities, treat each
problem the same as when you solve a regular equation.
***THE ONLY DIFFERENCE***: when you multiply or divide by a negative number, you MUST flip
the inequality symbol!
< changes to >
> changes to <
< changes to >
> changes to <
a) x + 5 > 5 b) -2 > n - 4 - 5 - 5
x > 0
+ 4+ 4
2 > n
n < 2
Example 2: Solve the inequality.
5 5(-3) (-3)
x > -9
c) 5x > -45 d) < 12 a-3
x > -36
2x + 4 > 24 -b - 2 > 8
- 4 - 4
x > 10
+ 2 + 2
b < -10
Example 3: Solve the inequality.
(-4) (-4)
n < 6 m > 0
4 + < 6 - 6 < -6m-4
n3
2x > 2022
-b > 10-1-1
- 4 - 4
n3
< 2 (3)(3)
+ 6 + 6
m-4
< 0
Example 4: Medical Problem
A nurse wants to give a patient medicine. She wants to give the patient the same dosage every 6 hours, but he cannot exceed 32 ml in a day. What is the maximum dosage that the nurse can give the patient each time?
If the patient receives a dosage every 6 hours, then how many
dosages will the patient get in one day?
4 dosages
4d < 32
44
d < 8
Each dosage can be a maximum of 8ml.