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Solving & GraphingInequalities

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 3: Solve two inequalities.

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You learned that an INEQUALITY compares using symbols:

Write this expression in words

1. (6)(7) (9)(5)

2. 66 ÷ 2 (8)(4)

3. – 3 – 7 – 3 + 7

Comparison Practice

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x ≥ 7

f ≤ 13

b > ½

5.9 < mk ≤ 100

WRITE THREE OF YOUR OWNALGEBRAIC INEQUALITIES

You learned that ALBEBRAIC INEQUALITIES contain Variables:

1.

2.

3.

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A SOLUTION makes the inequality TRUE.

1514 < The solution

(5)(3)14 The Inequality

Problem Written with Solution Circled

1) 34 17 ● 22) 54 ÷ 9 5

3) (16)(3) 23 + 18

Solve

?

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A SOLUTIONS SET is a RANGE of possible answers

“It anywhere from ____ to ____.

Inequality In Words What are 3 possible solutions? Why?

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

2) a ≤ -3

3) y > 11

Fill in the empty boxes

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How to write answers for a SOLUTION SET?Arrows & Points

f < 21. For ‘less than’, the arrow points down 2. When there is not an equals line, the point is open.

f ≥ 2

1. For ‘more than’, the arrow points up2. When there is an equals line, the point is closed.

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Practice

Inequality Solution Set

x ≤ -1

h > 10

w < -7

Graph the solution set for each inequality. Remember!

1) Which direction does the arrow go?

2) Is the point open or closed?

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One-Step Inequalities

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Solving for Inequalities is EXACTLY like EQUATIONS.YOU KNOW THIS SIDE! Solution Set

x + 7 = 10 x + 7 ≤ 10 - 7 = - 7 - 7 ≤ - 7x = 3 x ≤ 3

Equals lineclosed point

Q: Why don’t we graph the equation?A: We know the answer, it’s 4.

Q: Why do we graph the inequality?A: To show all possible answers.

We’re not sure exactly, but we know it’s 3 or lower.

Subtract 7From both

Sides.

Bring downwhat’s left.

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24 ≤ 6w

Example 1

a + 6 ≥ 8─ 6

a ≥

Example 2

w≤1. To solve, fill in the boxes above.2. Insert the appropriate open or

closed point below.

1. To solve, fill in the boxes above.2. Insert an arrow going in the correct

direction below.

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Example 3 Example 4

1. To solve, fill in the boxes above.2. Write the SOLUTION SET FOR

example 4 below.

1. To solve, fill in the boxes above.2. Insert an arrow going in the correct

direction below.

k ─ 2 < 3

k < >

w4

> -1 )()(

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PracticeInequality Solution Set

1. x + 6 > 15

2. y + 8 < 8

3. 5z ≤ 35

4. a – 7 ≥ 13

5. b 6 > 3

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Two-Step Inequalities

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Solving for 2 step Inequalities is EXACTLY like EQUATIONS.

YOU KNOW THIS SIDE! Solution Set

5x + 8 = 18 5x + 8 ≤ 18 - 8 = - 8 - 8 ≤ - 85x = 10 5x ≤ 105 5 5 5 x = 2 x ≤ 2

Q: Why don’t we graph the equation?A: We know the answer, it’s 2.

Q: Why do we graph the inequality?A: To show all possible answers. We’re

not sure exactly, but we know it’s 2 or lower.

Subtract 8From both

Sides.

Divide by 5 on both Sides.

18 < 6w + 6Example 1

5a ─ 5 > 10+ 5

a >

Example 2

Insert the appropriate open or closed point below.

Insert an arrow going in the correct direction below.

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5a > < 6w

< w

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Example 3 Example 4

2k + 12 ≤ 12

k ≥

w4

+ 5 ≥ 8

≤Write the SOLUTION SET FOR examples 3 and 4 below.

w

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PracticeInequality Solution Set

1. 3x + 14 > 38

2. 5y – 5 < 55

3. 3z – 15 ≤ 15

4. 3a – 3 ≥ 0

5. b 2 + 6 > 6