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

|x +17| = 15

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.

__

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