Lesson 11 Solving Absolute Value Inequalities

TEKS 2A.6F
We will solve Absolute value inequalities.
I will summarize how to solve absolute value inequalities algebraically.

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Lesson 11 Solving Absolute Value Inequalities

Multiple Choice

Formulate the absolute value equation from the problem in the picture.

• |x - 6.4| = 58.2

• |x - 400| = 6.4

• |x - 58.2| = 6.4

• |x - 400| = 58.2

Inequalities will be solved very similarly to equations. Graphing will look a little different and there will be some special cases we will look at.

Remember the definition of absolute value**

If we use the symbol ≥ or ≤ we will have a CLOSED circle on the graph

For symbols > or < the circle will be open for only that value.

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Key Idea:

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If you see this symbol, ≥, we will ​

Select answer

the circle on the graph.

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If you see this symbol <, we will ​

Select answer

the circle on the graph.

​equation

​equation

​equation

​equation

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​equation

If you see these cases, know how the definition of absolute value works to save time!!

​Don't waste time on these Special cases

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Don't waste time working out a problem like this: $$\left|x-2\right|$$ ​ < $$0$$ , because it is ​

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true.

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Don't waste time working out a problem like this: $$\left|x-2\right|$$ ​ ​

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$$-2$$ , because it is ​ always ​ true.

Fill in the Blanks

Find the solution(s) to the inequality.

Poll

Rate your understanding of solving absolute value inequalities:

• 4 - Great! I could definitely repeat this again

• 3 - Good, I could probably repeat this if I looked at notes

• 2 - Ok, I will need some practice

• 1 - Shaky, I'm having some trouble