Presentation about Graph Inequalities.ppt
- 1. Solving and Graphing Linear Inequalities Solving One-Step Linear Inequalities
- 2. What’s an inequality? • Is a range of values, rather than ONE set number • An algebraic relation showing that a quantity is greater than or less than another quantity. Speed limit: 75 55 x
- 3. Symbols Less than Greater than Less than OR EQUAL TO Greater than OR EQUAL TO
- 4. Solutions…. You can have a range of answers…… -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers less than 2 x< 2
- 5. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers greater than -2 x > -2
- 6. Solutions continued…. -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers less than or equal to 1 1 x
- 7. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5 All real numbers greater than or equal to - 3 3 x
- 8. Did you notice, Some of the dots were solid and some were open? -5 -4 -3 -2 -1 0 1 2 3 4 5 2 x -5 -4 -3 -2 -1 0 1 2 3 4 5 1 x Why do you think that is? If the symbol is > or < then dot is open because it can not be equal. If the symbol is or then the dot is solid, because it can be that point too.
- 9. Write and Graph a Linear Inequality Sue ran a 2-K race in 8 minutes. Write an inequality to describe the average speeds of runners who were faster than Sue. Graph the inequality. Faster average speed > Distance Sue’s Time 8 2 s 4 1 s -5 -4 -3 -2 -1 0 1 2 3 4 5
- 10. Solving an Inequality Solving a linear inequality in one variable is much like solving a linear equation in one variable. Isolate the variable on one side using inverse operations. Add the same number to EACH side. x – 3 < 5 Solve using addition: 5 3 x +3 +3 x < 8
- 11. Solving Using Subtraction Subtract the same number from EACH side. 10 6 x 4 x -6 -6
- 12. Using Subtraction… 3 5 x Graph the solution. -5 -4 -3 -2 -1 0 1 2 3 4 5
- 13. Using Addition… -5 -4 -3 -2 -1 0 1 2 3 4 5 4 2 n Graph the solution.
- 14. THE TRAP….. When you multiply or divide each side of an inequality by a negative number, you must reverse the inequality symbol to maintain a true statement.
- 15. Solving using Multiplication Multiply each side by the same positive number. 3 2 1 x 6 x (2) (2)
- 16. Solving Using Division Divide each side by the same positive number. 9 3 x 3 x 3 3
- 17. Solving by multiplication of a negative # Multiply each side by the same negative number and REVERSE the inequality symbol. 4 x Multiply by (-1). 4 x (-1) (-1) See the switch
- 18. Solving by dividing by a negative # Divide each side by the same negative number and reverse the inequality symbol. 6 2 x 3 x -2 -2
- 19. Homework Page 337 – 338 # 22-54 evens 55-60 61 & 65