2016 Fermat Problem 13

The numbers 4x, 2x-3, 4x-3 are three consecutive terms in an arithmetic sequence. What is the value of x?

(An *arithmetic sequence* is a sequence in which each term after the first is obtained from the previous term by adding a constant. For example, 3, 5, 7, 9 are the first four terms of an arithmetic sequence.)

\textbf{(A)}\ \frac{3}{4}\quad \textbf{(B)}\ -\frac{4}{3}\quad \textbf{(C)}\ \frac{3}{2}\quad \textbf{(D)}\ -\frac{3}{2}\quad \textbf{(E)}\ -\frac{3}{4}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Fermat contests here.