The solution of the equation $\frac{(x+1)-(2x+4)}{3-5x}=\frac{1}{23}$ is also the solution of the equation :

` as specified by the prompt constraints: - Use MathML / standard HTML formatting rules (no LaTeX `$..$`, standard raw Unicode, no display="block", etc.) - Wrap text in `

` and `` / ``. Let's output the result. 3 (2x + 3) = 5 (x + 1)

The correct option is 3 (2x + 3) = 5 (x + 1).

Step 1: Solve the given equation for $x$.

The given equation is:

$\frac{(x+1)-(2x+4)}{3-5x}=\frac{1}{23}$

Simplifying the numerator on the left-hand side:

$(x+1)-(2x+4)=x+1-2x-4=-x-3$

Substitute this back into the equation:

$\frac{-x-3}{3-5x}=\frac{1}{23}$

Cross-multiplying gives:

$23(-x-3)=1(3-5x)$

$-23x-69=3-5x$

Rearranging terms to isolate $x$:

$-23x+5x=3+69$

$-18x=72$

$x=\frac{72}{-18}=-4$

Step 2: Verify which given option has $x=-4$ as a solution.

Substitute $x=-4$ into the equation 3 (2x + 3) = 5 (x + 1):

LHS = $3\left(2\right(-4)+3)=3(-8+3)=3(-5)=-15$

RHS = $5\left(\right(-4)+1)=5(-3)=-15$

Since LHS = RHS, $x=-4$ is indeed the solution of 3 (2x + 3) = 5 (x + 1).