1. Solving and Graphing Linear Inequalities
Solving One-Step Linear Inequalities

2. rather than ONE set number
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.

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……
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

7. Solutions continued… -5 -4 -3 -2 -1 0 1 2 3 4 5
All real numbers greater than or equal to -3

8. Take Note! > Open Right < Left Closed Inequality Symbols
Open or Closed Circle
Left or Right Side
>
Open
Right
<
Left
Closed

9. Solving an Inequality x < 8 Solve using addition:
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.
Solve using addition:
x – 3 < 5
Add the same number to EACH side.
x < 8

10. Solving Using Subtraction
Subtract the same number from EACH side.

11. Using Subtraction…
Graph the solution.

12. Using Addition…
Graph the solution.

13. Solving using Multiplication
Multiply each side by the same positive number.
(2)

14. Solving Using Division
Divide each side by the same positive number. 3

15. 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.

16. Solving by multiplication of a negative #
Multiply each side by the same negative number and REVERSE the inequality symbol.
Multiply by (-1).
(-1)
See the switch

17. Solving by dividing by a negative #
Divide each side by the same negative number and reverse the inequality symbol. -2
x > -3

18. Board Drill
Solve the following inequalities.
x – 5 > 12

19. Board Drill
6x < 108

20. Board Drill
-7x > 42

21. Board Drill
4x – 7 < 61

22. Board Drill
3x – 7 < 8

23. Board Drill
6x – 7 > 2x + 17

24. Board Drill
- ½ x < 8

25. Seatwork x – 7 > 2 x + 3 < 1 x – 5 > 4 3x > 36 -5x < 40
Solve and graph the following inequalities.
x – 7 > 2
x + 3 < 1
x – 5 > 4
3x > 36
-5x < 40