Solve inequalities with radical functions Precalculus

Solve the following inequalities.

\left(2x-3\right)^{-1/4} \lt \sqrt2

\left(-\infty,\dfrac{13}{8} \right)

\left( -\dfrac{11}{8},\dfrac{3}{2} \right]

\left( \dfrac{13}{8},\infty \right)

\left[ \dfrac{3}{2},\dfrac{13}{8} \right)

\left(4x+1\right)^{-1/2} \lt 3

\left[ -\dfrac{1}{4},-\dfrac{2}{9} \right)

\left( -\dfrac{2}{9},\infty \right)

\left( -\infty,-\dfrac{2}{9} \right)

\left( -\infty,-\dfrac{1}{4} \right)

\left(3x-11\right)^{3/2} \leqslant 8

\left(-\infty,5 \right]

\left( \dfrac{11}{3},\infty\right)

\left[ \dfrac{11}{3},5 \right]

\left[ 5,\infty \right)

\left(2x+5\right)^{-1/3} \gt 2

\left[-\dfrac{5}{2} ,-\dfrac{39}{16}\right)

\left[ -\dfrac{5}{2}, \infty\right)

\left(-\dfrac{39}{16} ,\infty\right)

\left( -\dfrac{13}{2},\infty \right)

\sqrt{x-2} \lt 3

\left(-\infty,11\right)

\left[2{,}7\right)

\left[2,\infty\right)

\left[2{,}11 \right)

\sqrt{2x+5} \geqslant 4

\left[\dfrac{11}{2},\infty \right)

\left[-\dfrac{5}{2},\infty \right)

\left[-\dfrac{5}{2},\dfrac{11}{2} \right)

\left(-\infty,-\dfrac{5}{2} \right]

\sqrt{3x-8} \leqslant 5

\left[\dfrac{8}{3},\dfrac{17}{3} \right]

\left(-\infty,11 \right]

\left[\dfrac{8}{3},11 \right]

\left(-\infty,\dfrac{17}{3} \right]