1 / 32

Solving and Graphing Inequalities

CHAPTER 6 REVIEW. Solving and Graphing Inequalities. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to. “x < 5”.

jfrancisco
Télécharger la présentation

Solving and Graphing Inequalities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER 6 REVIEW Solving and Graphing Inequalities

  2. An inequality is like an equation, but instead of an equal sign (=) it has one of these signs: < : less than ≤ : less than or equal to > : greater than ≥ : greater than or equal to

  3. “x < 5” means that whatever value x has, it must be less than 5. Try to name ten numbers that are less than 5!

  4. -25 -20 -15 -10 -5 0 5 10 15 20 25 Numbers less than 5 are to the left of 5 on the number line. • If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right. • There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc. • The number 5 would not be a correct answer, though, because 5 is not less than 5.

  5. “x ≥ -2” means that whatever value x has, it must be greater than or equal to -2. Try to name ten numbers that are greater than or equal to -2!

  6. -2 -25 -20 -15 -10 -5 0 5 10 15 20 25 Numbers greater than -2 are to the right of 5 on the number line. • If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right. • There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc. • The number -2 would also be a correct answer, because of the phrase, “or equal to”.

  7. -25 -20 -15 -10 -5 0 5 10 15 20 25 Where is -1.5 on the number line? Is it greater or less than -2? -2 • -1.5 is between -1 and -2. • -1 is to the right of -2. • So -1.5 is also to the right of -2.

  8. Solve an Inequality w + 5 < 8 w + 5 + (-5) < 8 + (-5) All numbers less than 3 are solutions to this problem! w < 3

  9. More Examples 8 + r ≥ -2 8 + r + (-8) ≥ -2 + (-8) r ≥ -10 All numbers from -10 and up (including -10) make this problem true!

  10. More Examples x - 2 > -2 x + (-2) + (2) > -2 + (2) x > 0 All numbers greater than 0 make this problem true!

  11. More Examples 4 + y ≤ 1 4 + y + (-4) ≤ 1 + (-4) y ≤ -3 All numbers from -3 down (including -3) make this problem true!

  12. 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.

  13. -6 0 Example: • Subtract 5 from each side. • Divide each side by negative3. • Reverse the inequality sign. • Graph the solution. Solve: -3y + 5 >23 -5-5 -3y > 18 -3 -3 y < -6

  14. Try these: -x -x x + 3 > 5 -3 -3 x > 2 + 11 + 11 -c > 34 -1 -1 c < -34 1.) Solve 2x + 3 > x + 5 2.)Solve - c – 11 >23 3.) Solve 3(r - 2) < 2r + 4 3r – 6 < 2r + 4 -2r -2r r – 6 < 4 +6 +6 r < 10

  15. You did remember to reverse the signs . . . . . . didn’t you? Good job!

  16. Example: -2 -2 We turned the sign! - 4x - 4x Ring the alarm! We divided by a negative! + 6 +6

  17. Remember Absolute Value

  18. Ex: Solve 6x-3 = 15 6x-3 = 15 or 6x-3 = -15 6x = 18 or 6x = -12 x = 3 or x = -2 * Plug in answers to check your solutions!

  19. Ex: Solve 2x + 7 -3 = 8 Get the abs. value part by itself first! 2x+7 = 11 Now split into 2 parts. 2x+7 = 11 or 2x+7 = -11 2x = 4 or 2x = -18 x = 2 or x = -9 Check the solutions.

  20. Ex: Solve & graph. • Becomes an “and” problem -3 7 8

  21. Solve & graph. • Get absolute value by itself first. • Becomes an “or” problem -2 3 4

  22. -4 3 Example 1: This is an ‘or’ statement. (Greator). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. • |2x + 1| > 7 • 2x + 1 > 7 or 2x + 1 >7 • 2x + 1 >7 or 2x + 1 <-7 • x > 3 or x < -4

  23. 2 8 Example 2: This is an ‘and’ statement. (Less thand). Rewrite. In the 2nd inequality, reverse the inequality sign and negate the right side value. Solve each inequality. Graph the solution. • |x -5|< 3 • x -5< 3 and x -5< 3 • x -5< 3 and x -5> -3 • x < 8 and x > 2 • 2 < x < 8

  24. Case 1 Example: Absolute Value Inequalities and

  25. Case 2 Example: Absolute Value Inequalities or OR

  26. Absolute Value • Answer is always positive • Therefore the following examples cannot happen. . . Solutions: No solution

  27. Graphing Linear Inequalities in Two Variables • SWBAT graph a linear inequality in two variables • SWBAT Model a real life situation with a linear inequality.

  28. Some Helpful Hints • If the sign is > or < the line is dashed • If the sign is  or  the line will be solid When dealing with just x and y. • If the sign > or  the shading either goes up or to the right • If the sign is < or  the shading either goes down or to the left

  29. When dealing with slanted lines • If it is > or  then you shade above • If it is < or  then you shade below the line

  30. Graphing an Inequality in Two Variables Graph x < 2 Step 1: Start by graphing the line x = 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line.

  31. Graphing a Linear Inequality Sketch a graph of y  3

  32. Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y = -x + 3

More Related