Transcript Solving one and Two Step Inequalities

Math Journal 10-13
Solve for x.
1. 𝑥 − 17 = 25
3. 5𝑥 = 25
2.
𝑥
13
− 12 = 15
4. −14𝑥 + 5 + 2𝑥 = −4𝑥 − 3
Unit 3 Day 5: Solving One and
Two Step Linear Inequalities
Essential Questions: How do we graph linear
inequalities in one variable? How do we solve
one and two step linear inequalities?
Vocabulary
Inequality Signs (as read from left to right )
• < "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛“
• ≤ "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜"
• > "𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛"
• ≥ "𝑔𝑟𝑒𝑎𝑡𝑒𝑟 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜"
•
Graph of the Inequality: the set of points on a
number line that represent all solutions of the
inequality.
Graphing Linear Inequalities
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:
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
Graph :
x<2
-2 -1
0
1
2
3
-2 -1
0
1
2
3
x > -2
x<1
-2 -1
0
1
2
3
-2 -1
0
1
2
3
x>0
Example 1: Graph the inequality.
x > -7
x<1
-7
1
x ≥ -9
x ≤ 10
-9
10
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.
s > 73
73
Solving Linear Inequalities
When 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 <
Example 2: Solve the inequality.
a) x + 5 > 5
b) -2 > n - 4
-5 -5
+4
2>n
n<2
x>0
c) 5x > -45
5
5
x > -9
+4
d)
(-3)
a < 12
(-3)
-3
x > -36
Example 3: Solve the inequality.
2x + 4 > 24
-4 -4
-b - 2 > 8
+2 +2
2x > 20
2 2
-b > 10
-1 -1
x > 10
b < -10
n
4+
<6
3
-4
-4
m
- 6 < -6
-4
+6 +6
n
(3)
< 2 (3)
3
m
(-4)
< 0 (-4)
-4
n<6
m>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
4
4
d<8
Each dosage can be a maximum of 8ml.
Summary
Essential Questions: How do we graph linear inequalities
in one variable? How do we solve one and two step
linear inequalities?
Take 1 minute to write 2 sentences answering the
essential questions.