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**Inequality Symbols Topic: Solving Inequalities**

Name: Date: Period: Topic: Solving Inequalities Essential Question: What is the correlation between solving equations and solving inequalities? Warm-up: Name the following inequality signs: Inequality Symbols Less than Not equal to Less than or equal to Greater than or equal to Greater than

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Vocabulary: An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:

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Solving Inequalities by Adding or Subtracting

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**Solving the Inequality**

w + 5 < 8 Note: We will use the same steps that we did with equations, if a number is added to the variable, we subtract the same number to both sides.

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**All numbers less than 3 are solutions to this problem!**

Answer w + 5 < 8 w < 8 -5 w + 0 < 3 w < 3 All numbers less than 3 are solutions to this problem!

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**Now you try it! 8 + r ≥ -2 7 > x – 5 x - 2 > -2 4 + y ≤ 1**

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**Answers to Practice Problems:**

x - 2 > -2 4 + y ≤ 1 x > r ≥ -2 -8 y ≤ 1 - 4 x + 0 > 0 y + 0 ≤ -3 r + 0 ≥ -10 x > 0 y ≤ -3 w ≥ -10 All numbers from -10 and up (including -10) make this problem true! All numbers from -3 down (including -3) make this problem true! All numbers greater than 0 make this problem true!

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**Answers to Practice Problems:**

x + 2 ≤ 3 x - 5 > 7 x ≤ 7 - 2 x – > 7 + 5 x + 0 ≤ 5 x + 0 > 12 x ≤ 5 x > 12 12 5

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What do these means? x < 5 x ≤ 3 x > 4 x ≥ 2

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**How to graph the solutions**

> Graph any number greater than. . . open circle, line to the right < Graph any number less than. . . open circle, line to the left Graph any number greater than or equal to. . . closed circle, line to the right Graph any number less than or equal to. . . closed circle, line to the left x > 4 x < 5 x ≥ 2 x ≤ 3

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**Multiplying or Dividing**

Solving Inequalities by Multiplying or Dividing

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**Solving the Inequality**

< - 2 15b < 60

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**Answers x < - 8 15b < 60 15b < 60 b < 4 15 15 < - 2**

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**But wait there is one special case:**

That was easy!!! But wait there is one special case: Sometimes you may have to reverse the direction of the inequality sign!! That only happens when you multiply or divide both sides of the inequality by a negative number.

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**Solving the Inequality**

- 4r > 16

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**( ( ( ( Answers - 4r > 16 - 4r > 16 r < - 4 - 4 - 4**

m < - 10 - 4r > 16 - 4r > 16 r < - 4 - 4 - 4

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Solving Multi-Step Inequalities

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**Solving multi-step inequalities is like solving multi-step equations. **

If you can solve you can solve

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Remember:

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**Which graph shows the solution to 2x - 10 ≥ 4?**

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Now you try it! Page 181 (1 – 4, 8, 16, 20) 1) (x + 4) - 5(x - 1) < 5 -2x + 6 ≥ 3x – 4 3 (t + 1) – 4t ≥ - 5 5m - 8 > 12 -5x – 9 < 26 V.I.I. Anytime you multiply or divide both sides of an inequality by a negative number, you need to reverse the sign.

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**Brief Review of Inequalities**

Wrap-Up: Brief Review of Inequalities Add/subtract the same number on each side of an inequality Multiply/divide by the same positive number on each side of an inequality If you multiply or divide by a negative number, you MUST flip the inequality sign! Home-Learning: Page 175 (34), Page 176 (70), Page 181 (12, 21, 24), Page 189 (2, 4), Page 190 (20), Page 192 (59, 60)

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