Answer: \(\displaystyle -\frac73\lt x\lt -\frac17\).

Answer: \(\displaystyle -\frac73\lt x\lt -\frac17\).

Since both sides are non-negative, square both sides of the inequality:

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

Expanding gives

\(25x^2+40x+16\lt 4x^2-12x+9.\)

Bring all terms to the left:

\(21x^2+52x+7\lt 0.\)

Factorise:

\(21x^2+52x+7=(7x+1)(3x+7).\)

So

\((7x+1)(3x+7)\lt 0.\)

The critical values are

\(x=-\frac17,\qquad x=-\frac73.\)

The quadratic is negative between its two roots, so

\(-\frac73\lt x\lt -\frac17.\)