Math Journal 10-13Solve for x.1. 2.

3. 4.

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.

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.