1. 7.5
Linear Inequalities

2. 7.5 – Linear Inequalities Goals / “I can…” Graph linear inequalities
Write and use linear inequalities when modeling real – world situations

3. 7.5 – Linear Inequalities RECALL Graph x > 4 on a number line.
Graph y ≤ 2 on a number line. -4 -2 2 4 -4 -2 2 4

4. 7.5 – Linear Inequalities REMEMBER:
The type of dot on the number line is important.
Open DOT means NOT INCLUDED (> or <)
Closed DOT means INCLUDED (≤ or ≥)

5. Remember these symbols!!!!
Less than
Greater than
Less than or EQUAL TO
Greater than or EQUAL TO

6. 7.5 – Linear Inequalities
When graphing inequalities on the coordinate plane, we use a similar idea.
Dashed lines mean the same as open circles.
(> or <)
Solid lines mean the same as closed circles.
(≤ or ≥)

7. 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.

8. 7.5 – Linear Inequalities
Oh, and did I mention we have to shade a part of the graph?????
When considering shading, you shade the part of the graph that WORKS FOR THE EQUATION.

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

10. 7.5 – Linear Inequalities
Graph
x ≥ 3

11. 7.5 – Linear Inequalities
Graph
y ≤ 2x + 2

12. 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

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

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 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

16. Solving by dividing by a negative #
Divide each side by the same negative number and reverse the inequality symbol. -2

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

18. 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

19. Step 1: Put into slope intercept form
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

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