Exercises Involving Absolute Value Equations

1.  The absolute value equation |x - 2| = 5 can be looked at geometrically as the value of x such that the ___________ from x to 2 is 5.

2.  Explain why |x + 3| = -2 has no solution.

For exercises 3 through 6, determine whether the statement is true or false and explain your reasoning.

3.  The equation |ax - b| = c where a, b, and c are constants has either no solution, one solution, or two solutions.

4.  The equation |2x + 5| = -1 is equivalent to the statement 2x - 5 = 1 or 2x - 5 = -1.

5.  The expression |4x - 2| is equal to the expression |4x + 2| for all values of x.

6.  The equation |5x - 1| + 3  =  8 is equivalent to the statement
        (5x - 1) + 3  =  8 or (5x - 1) + 3  =  -8

For exercises 7 through 33, solve for x.  If there is no solution, state that there is no solution.

7.  |x| = 6

8.  |x| = 0

9.  |x| = -2

10.  |x - 4|  =  3

11.   |x + 5|  =  1

12.  |x + 2|  =  -5

13.  |x - 1| = 0

14.  |x + 2|  =  -10

15.  |3x - 5|  =  2

16.  |4x - 1|  =  1

17.  |5 - 2x|  =  3

18.  |1 - 6x|  =  2

19.  |2x - 4|  + 3 =  5

20.  |3x - 2| + 4  =  6

21.  |2x + 1| + 2  =  2

22.  |5x - 1|  + 4  =  3

23.  |0.5x + 0.2|  =  0.4

24.  |1.5x - 1.1|  =  0.1

25. 

26. 

27.  |2(x - 3) + 4|  =  5

28.  |4(2x - 3) - 1|  =  7

29.  3|x - 4| + 2  =  6

30.  5 - 2|4x + 7|  =  3

31.  |x|  =  |2x - 4|

32.  |x - 3|  =  |x - 5|

33.  |3x + 1|  =  |2x - 3|

34.  My sister and I are six years apart in age.  My sister is 44 years old.  Use an absolute value equation to find the possibilities for my age.

35.  The elevations of Greenpark and Forksmith differ by 1200 feet.  Use an absolute value equation and the fact that Forksmith's elevation is 2304 ft to find the possibilities for the elevation of Greenpark.

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