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Inequality Symbols

Explore the connection between solving equations and solving inequalities, learn symbol recognition and manipulation techniques, practice adding, subtracting, multiplying, and dividing to solve inequalities step by step. Master graphing solutions and solve multi-step inequalities confidently.

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Inequality Symbols

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  1. 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

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

  3. Solving Inequalities by Adding or Subtracting

  4. 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.

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

  6. Now you try it! 8 + r ≥ -2 7 > x – 5 x - 2 > -2 4 + y ≤ 1 x + 2 ≤ 3

  7. Answers to Practice Problems: x - 2 > -2 8 + r ≥ -2 4 + y ≤ 1 x - 2 + 2 > -2 + 2 4 - 4 + y ≤ 1 - 4 8 -8 + r ≥ -2 -8 y + 0 ≤ -3 x + 0 > 0 r + 0 ≥ -10 y ≤ -3 x > 0 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!

  8. 12 0 Answers to Practice Problems: x + 2 ≤ 3 x - 5 > 7 x + 2 - 2≤ 7 - 2 x – 5 + 5 > 7 + 5 x + 0 ≤ 5 x + 0 > 12 x ≤ 5 x > 12 5 0

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

  10. 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

  11. Solving Inequalities by Multiplying or Dividing

  12. Solving the Inequality < - 2 15b < 60

  13. Answers x > 4 x < - 8 < - 2 15b < 60 15b < 60 b < 4 15 15

  14. 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.

  15. Solving the Inequality - 4r > 16

  16. Answers ( ( ( ( m < - 10 - 4r > 16 - 4r > 16 r < - 4 - 4 - 4

  17. Solving Multi-Step Inequalities

  18. Solving multi-step inequalities is like solving multi-step equations. If you can solve you can solve

  19. Remember:

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

  21. Now you try it! Page 181 (1 – 4, 8, 16, 20) • 1) 3(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.

  22. 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 MUSTflip 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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