Show:
Linear Inequalities
Absolute Value Equations
Absolute Value Inequalities
Absolute Value Functions
100
This is the kind of line that you draw when you see a < sign when graphing a linear inequality like y < 2x.
What is a dashed line?
100
The absolute value of a number x, written |x|, is the distance the number is from _____ on the number line.
What is 0?
100
When I have an absolute value inequality, I need to rewrite the inequality as two linear inequalities. a. For the first inequality, I leave the constant on the other side as is. b. For the second inequality, I change the ___________ of the constant on the other side and ______ the inequality sign.
What is change the sign of the constant and flip the inequality sign?
100
An absolute value function always looks like a _______ shape.
What is a V shape?
200
If I have a linear inequality like 3x + 4y < 12, I need to put it in this form first so that I can graph it.
What is y < mx + b form (specifically y < (-3/4)x + 3)?
200
Because it is a distance, the absolute value of a number can never be __________.
What is negative?
200
I need to graph the inequality x < 2. I draw a circle at the point 2. Do I fill it in or leave it open?
What is leave it open?
200
We will plot the vertex of the absolute value function at the ___________.
What is the origin (0,0)?
300
I need to shade this side of y > 2.
What is the side above y = 2/the upper half-plane?
300
When I want to solve an absolute value equation, I need to rewrite the equation as two linear equations, with the absolute value expression on one side and a constant on the other. a. For the first equation, I leave the constant on the other side as is. b. For the second equation, I change the ___________ of the constant on the other side.
What is the sign?
300

Solve and graph the absolute value inequality |2x + 3| > 7.

What is x > 2 or x < -5?

300
Evaluate the function when x = 2 and x = ‐3 for h(x) = |2x + 9|
What is 13 and 3?
400
I am given the inequality x < 3. The line I draw at x = 3 is dashed and should be drawn vertically (straight up and down), horizontally (straight left and right), or neither?
What is vertically (straight up and down)?
400
When I solve an absolute value equation, I will end up with ______(a number) solutions.
What is two?
400

Solve and graph the following inequality:

|x+5|>9

x>4

x<-14

400
The function y = ‐2|x| opens _________ (a direction).
What is down?
500

Word problem: A hockey team will spend at most $500 to buy new elbow pads and mouth guards. Elbow pads cost $50 each and mouth guards cost $10 each. a) Write a linear inequality in two variables to represent the number of elbow pads and mouth guards the team can purchase. b) Graph the inequality.

What is 50e + 10m <= $500?

500
Solve the absolute value equation: |5 + 2x| = 13
What is x = 4, x = -9?
500

Solve and graph the following absolute value inequality:

4|3x-3|<24

x<3

x>-1

500

Graph y = 3|x| and tell whether it is narrower or wider than y = |x|.

What is narrower?