Question

Write the absolute value in the form |x-b|=c (where b is a number and c can be wither a number or and expression) that has the following solution set.

Two solutions: x=-2, x=-32

Answer 1

|x +17| = 15

Explanation:

The values that go into your absolute value equation template can be found by solving the template equation, then matching results to the desired solution values.

|x -b| = c

resolves to ...

x -b = c . . . . for x -b > 0

x = b+c

and

-(x -b) = c . . . for x -b < 0

x = b -c . . . . . solve for x

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The value of c must be positive, so the value b+c will be the most positive solution:

-2 = b +c . . . . . the most positive solution

-32 = b -c . . . . the most negative solution

Adding these equations gives ...

2b = -34 ⇒ b = -17

c = -2 -b . . . . from the first equation

c = -2 -(-17) = 15

Putting the found values b=-17, c=15 into the absolute value equation template gives ...

|x +17| = 15