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Intro to Inequalities

Materials Needed1. Individual Interactive Notebooks2. Pencil3. Answer Sheet

PS 4: Solve one- and two-step linear inequalities and graph the solutions on the number line.

LT 1: Graph solutions of inequalities on the number line.

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Definition: Inequality

in·e·qual·i·tyNoun: The relationship between two mathematical expressions that are

not equal.

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An INEQUALITY compares using these symbols: What are their labels?

Examples(do some solving first)

1

2

?

?

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Comparison Practice 5. 6 + 8 15

6. 6 + 4 8 + 4

7. (8)(3) (6) (4)

8. 16 ÷ 2 36 ÷ 4

9. 17 – 3 21 – 9

10.(4)(5) 23 – 7

1. 12 15

2. 43 68

3. 4 + 2 8

4. 4 12 ÷ 4

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Definition: Algebraic Inequality

al·ge·bra·ic in·e·qual·i·tyNoun: An inequality that contains a

variable

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ALGEBRAIC INEQUALITIES

x ≥ 7f ≤ 13

b > ½ 5.9 < mk ≤ 100

≥ 7s ≥

s 65

NOW WRITE YOUR OWNALGEBRAIC INEQUALITY

Examples1.

2.3.

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Now Write 5 more of your ownAlgebraic Inequalities

1.

2.

3.

4.

5.

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Definition: Solution

so·lu·tionNoun: 1) A means of solving a problem. 2) The correct answer to a puzzle.

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Sometimes we know the answer to an inequality. The number that makes the inequality true is call

the SOLUTION.

Example 1 21 - 614

1514

?

<

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Sometimes we know the answer to an inequality. The number that makes the inequality true is call

the SOLUTION.

Example 2 913 - 499

?

The solution is 9,This makes the inequality

TRUE.

=

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Find the Solution of each Inequality Circle the Solution you found.

Problem Written with Solution Circled

1) 24 17 + 4

2) 32 – 10 28

3) (12)(3) 30

4) 13 54 ÷ 9

5) 3x – 12 = 24 √64

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Definition: Solutions Set

so·lu·tion setNoun: The set of values that make a

mathematical statement true.

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A SOLUTIONS SET is a group of possible answers. We will never know

for sure what the answer will be, so we give a range of possible answers

It’s like saying: I’m not sure what the solution is

exactly, but it’s greater/less than __________.

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Use the completed squares to help you fill in the blank ones.

Inequality In Words What are 3 possible solutions? Why?

1) x < 5 • 32, -7, 3 • they are all less than 5

2) a > 0 • ‘a’ is greater than 0

3) y ≤ 13

4) m ≥ 3 • ‘m’ is greater than or equal to 3

• 3, 99, 1235• they are all greater than or equal to 3

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Here are 2 Examples of SOLUTION SET answers.

Inequality Solution Set Answer

x < 5

m ≥ -1

1 2 3 4 5 6 7 8

1 2 3 4-1 0-3 -2

X could be ANY number less than five,

but NOT 5

M could be ANY number greater than -1,

including -1.

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What do you write for an answer when trying to show a SOLUTION SET?

Inequality Solution Set1) x < 5

2) a > 0

3) y ≤ 13

4) m ≥ 3

1 2 3 4 5 6 7 8

1 2 3 4 5 6-1 0

1 2 3 4

1 2 3 4-1 0

-1 0-3 -2

5 6

Arrows & Points

For the ‘less than’ sign, the arrow points down the number line.

For the

‘greater than’

sign, the arrow

pointsup

the number line.

Arrows are logical.

Which Way Does the Arrow Go?

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What do you write for an answer when trying to show a SOLUTION SET?

Inequality Solution Set1) x < 5

2) a > 0

3) y ≤ 13

4) m ≥ 3

1 2 3 4 5 6 7 8

1 2 3 4 5 6-1 0

Find out why!

1 2 3 4

1 2 3 4-1 0

-1 0-3 -2

5 6

You notice that

at times the

beginning

point is open

and other

times the

beginning point

is closed.

Arrows & Points

Why are some Points Open, an Others Closed?

Why are points open & closed?

Inequality Solution Set

1) x ≤ 16

2) a > 3

3) y ≥ 0

4) m < 22

5) k ≤ 2

41 2 3-1 0 5 6

What pattern do you notice? When should you make the beginning point open?When should the beginning point be closed?

11 12 13 14 15 16 17

41 2 3-1 0 5 6

2421 22 2319 20 25

41 2 3-1 0 5 6

41 2 3-1 0 5 6

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What do you write for an answer when trying to show a SOLUTION SET?

Inequality Solution Set1) x > 4

2) a ≤ 2

3) y ≤ 3

4) m > -1

5) b ≥ 0

6) b < 0

1 2 4 5 6 7 8

You notice that the point is

open when there is

no equals line.

41 2 3-1 0 5 6

You notice that when there is

an equals line, the point is

closed.

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41 2 3-1 0 5 6

41 2 3-1 0-3 -2

41 2 3-1 0-3 -2

41 2 3-1 0-3 -2

Insert the correct

beginning point.

Insert the correct arrow.

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Solution Sets Practice

Inequality Solution Set

x ≤ 3

h > -2

w < -1

p ≥ -4

m ≥ -5

y < 12

a ≤ -7

t > 21

Graph the solution set for each inequality.

Remember!1) Which direction does

the arrow go?

2) Is the point open or closed?