Solve for the value of \( x \) in the matrix below: \( \left[\begin{array}{c}4 x \\ 5\end{array}\right]=\left[\begin{array}{c}15+x \\ 2 y\end{array}\right] \) \( x=2.5 \) \( x=4 \) \( x=5 \) \( x=19 \)

To solve for the value of \( x \) in the matrix equation \[ \left[\begin{array}{c}4 x \\ 5\end{array}\right]=\left[\begin{array}{c}15+x \\ 2 y\end{array}\right], \] we can set up a system of equations from the corresponding elements of the matrices: 1. From the first component: \( 4x = 15 + x \) 2. From the second component: \( 5 = 2y \) We can solve the first equation for \( x \): \[ 4x - x = 15 \\ 3x = 15 \\ x = 5. \] Now, we can check which \( x \) value matches \( x = 5 \): So the value of \( x \) is \( 5 \). Thus, the answer from the given options would be: **x = 5**