Unit 4 Summary
Class: Algebra 1
Unit 4: Inequalities and Absolute Value Functions – Chapter 6
I. Big Ideas:
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Students will understand how to interpret and determine the reasonableness of solutions to
inequalities and systems of inequalities.
Students will understand how to analyze situations involving linear functions and formulate
inequalities to solve real-world problems.
Students will be able to represent solution sets for inequalities symbolically as intervals or
graphically on a number line.
II. Topics that will be covered:
1.
2.
3.
4.
5.
6.
7.
8.
III.
Solving inequalities
Solving multi-step inequalities
Solving compound inequalities
Absolute-value functions
Solving absolute-value equations
Solving absolute-value inequalities
Graphing absolute-value functions
Systems of inequalities
Essential Questions:
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How is solving inequalities the same/different from solving equations?
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How does solving inequalities apply to the real-world?
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What is special about when you multiply and divide in an inequality problem compared to when you
add and subtract?
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What makes a compound inequality different from a simple inequality?
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How can inequalities be written and graphed to represent real-life situations?
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Why does an absolute-value function have more than one answer?
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What is a vertex?
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How do numbers in the absolute-value function affect where it is graphed on the coordinate plane?
IV.
Sample questions to answer by the end of the unit:
Solve and graph each inequality.
1. –12  2x + 4 ≤ 20
2. 2x – 3  19 or 45  8x – 3
3. 7x - 14  7
4. 8 + 2x + 6 ≤ 22
5. For what values of x will the rectangle have an area of less than 500 feet2.
8
3X - 7
6. An obtuse angle measure is (3x + 12). What are the possible values of x to make this a true statement?
Write and solve an inequality to support your answer.
7. Write an absolute value equation that has one answer and explain why it would have only one solution.
8. According to a height and weight chart, Margo’s ideal weight is 120 pounds. She wants to stay within 7
pounds of her ideal weight. Write an absolute-value inequality to describe the acceptable weights. What is
the solution of your inequality?
Write a function for each transformation of y = │x│ described below.
9. The graph is translated 3 units to the left and 12 units up.
10. The graph is translated 4 units down and 5 units to the left.
11. The graph is reflected across the x-axis and translated to the right 2 units.
In what way would the graph of y = │x│ move according to the following equations? Be specific.
12. y = │x + 3│- 5
13. y =│x - 2│ + 7
14. On his last three tests, Michael scored a 93%, 72%, and 88%. If he wants his test average to be an 87%
or higher, what does he need to scored on the fourth test?
Graph each absolute value function.
15. y = x + 6 - 4
16. y = 2x + 1 + 2