\( \llbracket 2 x - 3 \rrbracket = - 5 \)

To solve the equation \( \llbracket 2x - 3 \rrbracket = -5 \), we need to find the range of values for \( x \) such that the expression \( 2x - 3 \) is equal to -5. The notation \( \llbracket \cdot \rrbracket \) typically denotes the greatest integer function, which rounds down to the nearest integer. However, since the right-hand side of the equation is -5, which is an integer, we can assume that the greatest integer function is not affecting the equation. So, we have: \[ 2x - 3 = -5 \] Now, let's solve for \( x \): \[ 2x = -5 + 3 \] \[ 2x = -2 \] \[ x = \frac{-2}{2} \] \[ x = -1 \] Since the right-hand side is an integer and the greatest integer function is not affecting the equation, the solution is \( x = -1 \). This is the only value of \( x \) that satisfies the equation \( \llbracket 2x - 3 \rrbracket = -5 \).