Compare and contrast the solution of |2x + 3| > 9 and the solution of |4x + 6| > 18.

A. The first absolute value equation has no solution, while the second equation does.

B. The first absolute value equation has a solution, while the second one does not. C. Both absolute value equations have the same solution

D. Neither absolute value equation has a solution.

I'd suggest attempting to solve both equations.

|2x + 3| > 9 can be simplified by dividing all terms by 2: |x + 3/2| > 9/2. The solution is centered at - 3/2, and consists of x (-3/2+9/2), or

x 6/2, which reduces to x 3.

The solution set for |4x + 6| > 18 is found in the same way. Simplify this by dividing all three terms by 4, obtaining |x + 6/4| > 18/4, or |x + 3/2| > 9/2.

This is precisely the same result as that found for the previous inequality.

The correct response is "C. Both absolute value equations have the same solution."