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8-2-7. Absolute Value

Name _____________________________________________________   Date __________________    Score _________

Keywords: Math-8-2-7

Questions

1.
Solve: |x|=6
Hint: First case: x=6, Second case: x=−6
20 points
 
2.
Solve: 9=|x+5|
20 points
 
3.
Solve: 2|x|=18
40 points
 
4.
Solve: |x|=0
20 points
 
5.
Solve: |x−3|−6=2
40 points
 
6.
Solve: 7=|3x+9|+7
60 points
 
7.
Solve: 5|x+7|+14=8
Hint: If after simplifying the equation, it does not makes sense, what can you conclude?
80 points
 
8.
Solve: −|x|=15
80 points
 
9.
Solve: 18=3|x−1|
80 points
 
10.
Solve: 3|x|−12=18
80 points
 
11.
Solve: |23x−23|=23
80 points
 
12.
Solve: |−2x+3|=5.8
80 points
 
13.
Solve: 8=7−|x|
Hint: If after simplifying the equation, it does not makes sense, what can you conclude?
80 points
 
14.
Solve: |x−3|+14=5
Hint: If after simplifying the equation, it does not makes sense, what can you conclude?
80 points
 
15.
Solve: 3+|x−1|=3
Hint: If after simplifying the equation, it does not makes sense, what can you conclude?
80 points
 
16.
Two numbers that are 5 units from 3 on the number line are represented by the equation |n−3|=5. What are these numbers?
80 points
 
17.
An inspector at a bolt factory checks bolts that come off the assembly line. Any bolt with a diameter that differs by more than 0.04 mm from the 6.5 mm is sent back. Write and solve an absolute value equation to find the maximum and minimum diameters of the acceptable bolts.
Hint: |x− center|= tolerance
80 points
 
Possible Points: 1080
 

Solutions

  1. x={−6,6}
  2. x={−14,4}
  3. x={−9,9}
  4. x=0
  5. x={−5,11}
  6. x={−3}
  7. No solution.
  8. x=−15
  9. x={−5,7}
  10. x={−10,10}
  11. x={0,2}
  12. x={−1.4,4.4}
  13. No solution
  14. No solution
  15. x=1
  16. n={−2,8}
  17. |x−6.5|=0.04 x={6.54 mm,6.46 mm}Two solutions.