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Warm-Up

Warm-Up . Graphing Inequalities. SCOS 4.01. Objective The student will be able to:. graph inequalities on a number line. solve inequalities using addition and subtraction. Designed by Skip Tyler, Varina High School. Symbols and Meanings. Inequalities. Equalities. <. Is less than. =.

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Warm-Up

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  1. Warm-Up

  2. Graphing Inequalities SCOS 4.01

  3. ObjectiveThe student will be able to: • graph inequalities on a number line. • solve inequalities using addition and subtraction. Designed by Skip Tyler, Varina High School

  4. Symbols and Meanings Inequalities Equalities < Is less than = Equals- is the same as Is greater than > Congruent- same size and shape Is less than or equal to Is greater than or equal to ~ Similar- same shape Approx. equal to Not equal to =

  5. Not Equal

  6. Graphing Symbols

  7. Checking Solutions of Equations Decide whether 4 is a solution of the inequality.

  8. When you graph inequalities that have only one variable, we use a number line. We will use open and closed circles and arrows pointing to the left or right to graph our answers. Take a look at the model below.

  9. x<-3

  10. o 1) Graph the solution set ofx < 3. When you have < or >, use an open dot!

  11. • 2) Graph the solution set ofy ≥ -5/4. When you have ≤ or ≥, use a closed dot! Converting -5/4 to a decimal = -1.25

  12. o 3) Graph the solution set ofp ≠ 2. When you have ≠, use an open dot and shade both ways!

  13. White Board 1-6

  14. White Board 7-12

  15. White Board 13-18

  16. Write an inequality

  17. Write an inequality

  18. Write an inequality

  19. Write an inequality

  20. Answer Now 4) Which inequality would have a closed dot on the number line? • > • < • ≥ • ≠

  21. Answer Now 5) Which inequality does NOT use an open dot on the number line? • ≤ • < • > • ≠

  22. o 29 30 31 6) Solve x + (-14) < 16 • Solve this problem like an equation • Draw “the river” • Eliminate double signs • Add 14 to both sides • Simplify • Check your answer • Graph the solution x- 14< 16 + 14 + 14 x < 30 30 + (-14) = 16 16 = 16

  23. ● -15 -14 -13 7) Solve y + 21 ≥ 7 • Draw the “river” • Subtract 21 from both sides • Simplify • Check your answer • Graph the solution - 21 -21 y ≥ -14 (-14) + 21 = 7 7 = 7

  24. o 16 17 18 8) Solve 8y + 3 > 9y - 14 - 8y - 8y 3 > y - 14 + 14 + 14 17 > y y < 17 8(17) + 3 = 9(17) - 14 • Draw “the river” • Subtract 8y from both sides • Simplify • Add 14 to both sides • Simplify • Rewrite inequality with the variable first • Check your answer • Graph the solution

  25. o 6 7 8 o 6 7 8 ● 6 7 8 6 7 8 Answer Now 9) What is the graph of 7 ≤ m? ●

  26. ● 30 31 32 - 2r - 2r r – 17 ≥ 14 + 17 + 17 r ≥ 31 3(31) - 17 = 2(31) + 14 • Draw “the river” • Subtract 2r from both sides • Simplify • Add 17 to both sides • Simplify • Check your answer • Graph the solution 10) Solve 3r - 17 ≥ 2r + 14

  27. Answer Now 11) Solve -2x + 6 ≥ 3x - 4 • x ≥ -2 • x ≤ -2 • x ≥ 2 • x ≤ 2

  28. Answer Now 12) Joanna’s tests were 87, 93, 88 and 94. What must her 5th grade be to get a total of at least 459? • 96 • 97 • 98 • 100

  29. Your scores on the last three tests were 82, 87, and 74. Your score on the next test is x points. Do the following values for x give you at least 320 total points? a. 75 points b. 81 points Yes No

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