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.

|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