Unit 5: Day 5: Students will be able to graph linear inequalities.

Objective: Students will be able to graph linear inequalities.

Step 1: Simplify the inequality you're going to graph. Multiply out anything that's in parentheses, and combine numbers that are unattached to variables.
-2x² + 5x < -6(x + 1)
-2x² + 5x < -6x - 6

Step 2: Move all terms to one side so the other is zero. It will be easiest if the highest power variable is positive. Combine common terms (such as -6x and -5x).

0 < 2x² -6x - 5x - 6
0 < 2x² -11x - 6

Step 3:  Solve for the variables. Pretend that the inequality sign is an equal sign, and find all values of the variable. If necessary, solve by factoring.

0 = 2x² -11x - 6
0 = (2x + 1)(x - 6)
2x + 1 = 0, x - 6 = 0
2x = -1, x = 6
x = -1/2, x = 6

Step 4: Draw a number line including the variable solutions (in order).

Step 5: Draw a circle on the points. If the inequality symbol is "less than" (<) or "more than" (>), draw an empty circle over the variable solution(s). If it means "less than or equal to" (≤) or "more than or equal to" (≥), then fill in the circle.

In this case the equation was greater than zero, so use open circles.

Step 6: Test your solution. Take a number from each of the resulting intervals and plug it back into the inequality. If you get a true statement once solved, shade this region of the number line.

In the interval from (-∞,-1/2) we will take -1 and plug it into the original inequality.
0 < 2x² -11x - 6
0 < 2(-1)² -11(-1) - 6
0 < 2(1) + 11 - 6
0 < 7
Zero is less than 7 is correct, so shade (-∞, -1/2) on the number line.

Next, on the interval from (-1/2, 6) we will use zero.
0 < 2(0)² -11(0) - 6
0 < 0 + 0 - 6
0 < -6
Zero is not less than negative six, so do not shade (-1/2,6).

Lastly, we will take 10 from the interval (6,∞).
0 < 2(10)² - 11(10) + 6
0 < 2(100) - 110 + 6
0 < 200 - 110 + 6
0 < 96
Zero is less than 96 is correct, so shade (6,∞) as well.

Use arrows on the end of shading to indicate that the interval continues into infinity. The completed number line:

Questions:
 
1.) Graph the following inequality  y x + 3 

2.)

Which inequality is represented by the graph below?
 

Choose:

3.) Graph the following inequality:

2x + y > 4

 

 

 

 

 

 

Answers:

 

 

1.)

2.) y<-2x+1


3.)