Download Solve each equation. Check for extraneous solutions. 1. |3 – w| + 6

Algebra 2 Pre-AP
WS 2.1 Absolute Value Equations
Name ______________________________
Date __________________ Period _______
Solve each equation. Check for extraneous solutions.
1. 1 |3 – w| + 6 = 9
2. |2x| = 3x – 1
4. |y + 7| = 2y + 5
5.
2
3. |2z – 5| = 4z – 3
1
3w  2  3  3w  4
2
6. 2|4x – 1| + 5 = 15
Is the absolute value equation always, sometimes, or never true? Explain.
7.
|x| = –x
8. |z + 1| = z – 1
9. |5w + 3| = –4
Write an absolute value equation to describe each graph.
10.
11.
Write an absolute value equation that has the given solutions.
13. No solution
14. Infinitely Many Solutions
12.
15. You and your friends Jose and Sarah all live on the same street. You know that Jose lives five
blocks away from you. Jose says that Sarah lives two blocks from him, but he didn’t say whether she
lives closer to you than he does or further. Let b be the number of blocks Sarah might live from you.
Formulate an absolute value equation to represent this situation.
16. The amount of pretzels a snack food company fills each bag with must be within three pretzels of
the 100 pretzels expected per bag. A quality control inspector must ensure the bags are adequately
filled. Let p be the number of pretzels in each bag. Formulate an absolute value equation to represent
this situation.
_____ 17 . Jake's morning run was a distance of 9.3 miles. He ran back and forth on one long straight
street. He started at his house and ran to the school 4 miles away. Then he ran to the library, and then
he ran back to his house. What are possible distances the library could be from the house?
A. 4.65 mi
B. 1.3 mi
C. 1.3 mi, 4.65 mi
D. 0.65 mi, 4.65 mi
18. Error Analysis A small group of students is asked to solve the equation
|3x| = 5x + 4. Cheyenne shares the following solution with her group.
Identify the error(s) in Cheyenne’s work and provide a correct solution.
|3x| = 5x + 4
3x = 5x + 4 or –3x = –5x + 4
–2x = 4 or 2x = 4
x = –2 or x = 2
Pearson Texas Algebra II
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