Answer: \(-4\lt x\lt -2\).

Answer: \(-4\lt x\lt -2\).

Expand both sides:

\((2x+3)(x-4)=2x^2-5x-12,\)

and

\((3x+4)(x-1)=3x^2+x-4.\)

So

\(2x^2-5x-12\gt 3x^2+x-4.\)

Bring all terms to one side:

\(0\gt x^2+6x+8.\)

Hence

\(x^2+6x+8\lt 0.\)

Factorise:

\((x+2)(x+4)\lt 0.\)

The product is negative between the two roots, so

\(-4\lt x\lt -2.\)