1. Math Journal 10-13 𝑥−17=25 2. 𝑥 13 −12=15 3. 5𝑥=25 4. −14𝑥+5+2𝑥=−4𝑥−3
Solve for x.
𝑥−17= 𝑥 13 −12=15
3. 5𝑥= −14𝑥+5+2𝑥=−4𝑥−3
Math Journal 10-13

2. 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?

3. Vocabulary < "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛“ ≤ "𝑙𝑒𝑠𝑠 𝑡ℎ𝑎𝑛 𝑜𝑟 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜"
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.

4. 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: Graph :
All real numbers less than 2 1 2 3 -1 -2
x < 2
All real numbers greater than -2
x > -2 1 2 3 -1 -2
All real numbers less than or equal to 1 1 2 3 -1 -2
x < 1
All real numbers greater than or equal to 0
x > 0 1 2 3 -1 -2

5. s > 73 x ≥ -9 x ≤ 10 Example 1: Graph the inequality.
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
x ≤ 10 -9 10
s > 73 73

6. 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 <

7. a) x + 5 > 5 b) -2 > n - 4 Example 2: Solve the inequality. - 5
+ 4
+ 4
2 > n
x > 0
n < 2
c) 5x > d) < 12 a -3
(-3)
(-3) 5 5
x > -9
x > -36

8. Example 3: Solve the inequality.
2x + 4 > b - 2 > 8
- 4
- 4
+ 2
+ 2
2x > 20
-b > 10 2 2 -1 -1
x > 10
b < -10
< < -6 m -4 n 3
- 4
- 4
+ 6
+ 6 n 3
< 2 m -4
< 0
(3)
(3)
(-4)
(-4)
n < 6
m > 0

9. 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.

10. 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.