Solve the following absolute value equation. If needed, write your answer as a fraction reduced to lowest terms. \[ |4 x-9|=15 \] Answer 2 Points Selecting an option will display any text boxes needed to complete your answer. No Solution $(\varnothing)$ One Solution Two Solutions

Step 1 ：The absolute value of a number is its distance from zero on the number line. Therefore, an absolute value equation has two possible solutions: one where the quantity inside the absolute value is positive, and one where it is negative. So, the equation \(|4x - 9| = 15\) can be rewritten as two separate equations: \(4x - 9 = 15\) and \(4x - 9 = -15\).

Step 2 ：Solving the first equation \(4x - 9 = 15\), we get the solution \(x = 6\).

Step 3 ：Solving the second equation \(4x - 9 = -15\), we get the solution \(x = -\frac{3}{2}\).

Step 4 ：Final Answer: The solutions to the equation are \(x = 6\) and \(x = -\frac{3}{2}\). Therefore, the equation has \(\boxed{\text{Two Solutions}}\).