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Inequalities

Inequalities. Objective: Use inequalities. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12 7. 5-Minute Check. Solve each equation using the inverse operation. 5 + r = 12 7 34 = 2s.

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Inequalities

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  1. Inequalities Objective: Use inequalities

  2. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12

  3. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7

  4. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s

  5. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17

  6. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12

  7. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84

  8. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32

  9. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69

  10. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable.

  11. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites

  12. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation.

  13. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000

  14. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites.

  15. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites. 700

  16. 5-Minute Check • Solve each equation using the inverse operation. • 5 + r = 12 7 • 34 = 2s 17 • 7 = g/12 84 • 4.37 = y – 9.32 13.69 • Astronomers keep track of about 7000 objects. One out of every ten of these is a satellite. The rest are “space trash.” About how many satellites are astronomers tracking? • Define a variable. s = satellites • Write an equation. 10s = 7000 • Solve for the number of satellites. 700 • Check your solution.

  17. Real Life Examples • Inequalities are all around us! • What are some examples? Sliding pay scales Weight requirements Height requirements Speed limits Grades Capacity

  18. From Words to Symbols Inequality Symbols

  19. Graphing Inequalities on a Number Line • Steps: • Draw a number line • Put a circle around the number • If it includes “equal to” (£ , ³) fill in the dotRemember: Solid line, solid dot • Draw an arrow to the end of the number line making the statement true • Check your solution!

  20. Example • Graph x < 4 on a number line

  21. Example • Graph x < 4 on a number line When the variable is on the LEFT, the arrow points the same way as the inequality!

  22. Write an inequality using a number line

  23. Like equations, inequalities can either be true or false • Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15

  24. When solving inequalities, do the same steps as solving equations • Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 Plug it in!

  25. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 Simplify!

  26. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • Is 8 greater than 16? • This sentence is false.

  27. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24

  28. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 Plug it in!

  29. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 Simplify!

  30. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 • 16 ³ 15

  31. Example • For the given value, state whether each inequality is true or false. • x – 7 > 16, x = 15 • 15 – 7 > 16 • 8 > 16 • This sentence is false. • 16 ³2h/12 + 11, h = 24 • 16 ³2*24/12 + 11 • 16 ³ 4 + 11 • 16 ³ 15 • This sentence is true.

  32. Compound Inequalities • Compound inequalities are two inequalities considered together. • A compound inequality containing the word and is true only if both inequalities are true. This type of compound inequality is called a conjunction. • A compound inequality containing the word or is true if either of the inequalities is true. This type of compound inequality is called a disjunction.

  33. Examples • Examples of conjunctions: • x > -5 and x <1 • y < 3 and y > -3 • Examples of disjunctions: • x > -5 or x > 1 • y < 3 or y > -3

  34. Writing Compound Inequalities • When you see “and”, think of a sandwich! • x > -5 and x <1 is written -5 < x < 1 • y < 3 and y > -3 is written -3 < y < 3 • Hint: Graph each inequality separately, and see where they overlap!

  35. What is the compound inequality?

  36. What is the compound inequality?

  37. What is the compound inequality?

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