Solving and Graphing Absolute Value Inequalities

Absolute Value Inequalities

LO: I can ​graph absolute value inequalities

By MAURISA LEE VAN AS

Starter Activity

Inequality Check

Let's review important facts about graphing inequalities

Multiple Choice

If the inequality symbol is  $$<$$  or  $$>$$ , the line will be _________.

• solid

• dotted

Multiple Choice

If the inequality symbol is  $$>$$  or  $$\ge$$  you shade ________.

• above

• below

Multiple Choice

Is the point (1, 2) a solution for the following inequality? Choose the best answer that has the best explanation.

• Yes because it is located in the shaded region.

• No because it is located on the line and the line is dotted.

• Yes because it is located on the line.

• No because it is in the shaded region.

Multiple Choice

Write the absolute value inequality represented in the graph.

• $$y\ \ge\left|x+2\right|+1$$

• $$y\ \le\left|x-2\right|-1$$

• $$y\ \ge\left|x-2\right|+1$$

• $$y\ <\left|x-2\right|+1$$

Review Absolute Value Function

I DO:

​y < I x+1 l

WE DO:

​y > l x - 1 l +2

YOU DO!

Lets review what we've learnt by answering a few questions​

Multiple Choice

Is the line for the inequality

y ≥ |x+3|- 9 going to solid or dotted?

• Dotted

• Solid

Multiple Choice

Write the absolute value inequality represented in the graph.

• $$y\ge\left|x+2\right|+1$$

• $$y\le\left|x-2\right|-1$$

• $$y\ge\left|x-2\right|+1$$

• $$y<\left|x-2\right|+1$$

Multiple Choice

Are we going to shade above or below for y ≤ |x|+1?

• Above

• Below

Poll

How do you feel about solving absolute value inequalities?

• Stop! I don't understand at all!

• I mostly understand but I need more guidance

• I got it! Give me an extension task!

​Homework:

Graph the absolute value inequality based on your answer on the poll

Make sure to show your points, use the correct line and shade the correct area ​

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