Question

Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that have the following solution sets: Two solutions: x=−2, x=−32.

Answer 1

Answer:

  |x +17| = 15

Step-by-step explanation:

The absolute value equation ...

  |x -b| = c

can be rewritten as two equations:

  x -b = -c

  x -b = c

The solution to the first is x = b -c.

The solution to the second is x = b +c.

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The first solution is the smaller of the two, so we have ...

  b -c = -32

  b +c = -2

Adding these two equations gives ...

  2b = -34   ⇒   b = -17

Subtracting the first equation from the second gives ...

  2c = 30   ⇒   c = 15

The the equation you seek is ...

  |x +17| = 15