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INEQUALITIES

INEQUALITIES. Targeted TEKS: A.10 The student understands there is more than one way to solve a Quadratic Equation and solves them using appropriate methods. (A) Solve Quadratic Equations using concrete models, tables, graphs, and algebraic methods. Equal or Unequal?.

bradley-sheppard
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INEQUALITIES

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  1. INEQUALITIES Targeted TEKS: A.10 The student understands there is more than one way to solve a Quadratic Equation and solves them using appropriate methods. (A) Solve Quadratic Equations using concrete models, tables, graphs, and algebraic methods

  2. Equal or Unequal? • We call a math statement an EQUATION when both sides of the statement are equalto each other. • Example: 10 = 5 + 3 + 2 • We call a math statement an INEQUALITY when both sides of the statement are not equal to each other. • Example: 10 = 5 + 5 + 5

  3. Inequality Signs • We don’t use the = sign if both sides of the statement are not equal, we use other signs. > > < <

  4. DON’T FORGET THIS!!! • THE BIGGER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE BIGGER # • THE SMALLER SIDE OF THE SIGN IS ON THE SAME SIDE AS THE SMALLER # • Examples: 10 15 or -4 -12 < >

  5. Let’s Try Some! < < • 2 7 • -65 -62 • 32.3 32.5 • 3 5 • 22 10 • -10 4 > < < <

  6. Our Friend, The Number Line • A number line is simply this… …a line with numbers on it. • We use a number line to count and to graphically show numbers. • Example: Graph x = 5.

  7. Graphing Inequalities • Graph x = 2 • Graph x < 2 • Graph x < 2 • Graph x > 2 • Graph x > 2 A “closed” circle ( ) indicates we include the number. An “open” circle ( ) indicates we DO NOT include the number. By shading in the number line we are indicating that all the numbers in the shade are also possible answers.

  8. You Try This… • Graph x < 10

  9. You Try This… • Graph x > -4

  10. You Try This… • Graph x > 200

  11. You Try This… • Graph 7 < x

  12. Let’s Go Shopping! • Last week you went shopping at the mall. You had $150 to spend for the day. You bought a shirt for $25 and some jeans for $40. You also spent $5 on lunch. You wanted to purchase a pair of shoes. What is the maximum amount of money you could have spent on the shoes? $150 >$25 + $40 + $5 + x The cost of the shoes The maximum amount you have The amount you have spent

  13. How much can the shoes cost? $150 >$25 + $40 + $5 + x • Basically, the shoes must cost less than or equal to the amount you have left! $150 >$70 + x -$ 70 -$70 $ 80 > x The cost of the shoes

  14. Do You Really Understand? • Let’s see if this makes sense… (If we add 6 to both sides, is the inequality true?) 3 < 9 3+6 < 9+6 9 < 15 YES!

  15. Do You Really Understand? • Let’s see if this really makes sense… (If we subtract 3 from both sides, is the inequality true?) 10 > 4 10-3 > 4-3 7 > 1 YES!

  16. Do You Really Understand? • Let’s see if this still really makes sense… (If we multiply both sides by 2, is the inequality true?) 8 < 12 8(2) < 12(2) 16 < 24 YES!

  17. Do You Really Understand? • Let’s see if this still really makes sense… (If we multiply both sides by -2, is the inequality true?) 8 < 12 8(-2) < 12(-2) THIS STATEMENT IS NOT TRUE. WE NEED TO FLIP THE INEQUALITY SIGN TO MAKE THIS A TRUE STATEMENT. -16 < -24 -16 > -24

  18. Solving Inequalities • So apparently there are a few basic rules we have to follow when solving inequalities. • If you break these rules you will answer the question incorrectly! • DON’T BREAK THE RULZ!

  19. Rule #1 • Don’t forget who the bigger number is! • Example: 9 > x • It is okay to rewrite this statement as x < 9 • If 9 is bigger than “x”, that means that “x” is smaller than 9.

  20. Rule #2 • When multiplying or dividing by a negative number, reverse the inequality sign. • Example: 15 > -5x -5 -5 -3 < x

  21. Solve Each Inequality & Graph Example 1: m + 14 < 4 -14 -14 m < -10

  22. Solve Each Inequality & Graph Example 2: 6y - 6 > 7y -6y -6y -6 > y y < -6

  23. Solve Each Inequality & Graph Example 3: k < 10 (-3) (-3) -3 k > -30

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