If begin vmatrix 5 amp 3 x amp 2 end vmatrix be... - JAMB Mathematics 2024 Question

We are given the equation of two 2x2 determinants:

\(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} = \begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix}\)

First, we calculate the determinant of the left-hand side:

\(\begin{vmatrix} 5 & 3 \\ x & 2 \end{vmatrix} = (5 \times 2) - (3 \times x) = 10 - 3x\)

Now, calculate the determinant of the right-hand side:

\(\begin{vmatrix} 3 & 5 \\ 4 & 5 \end{vmatrix} = (3 \times 5) - (5 \times 4) = 15 - 20 = -5\)

Now, equate both determinants:

10 - 3x = -5

Solve for \(x\):

Subtract 10 from both sides:

-3x = -5 - 10

-3x = -15

Now, divide by -3:

x = \(\frac{-15}{-3} = 5\)

Thus, the value of \(x\) is 5.

The correct option is x = 5.