I know this has something to with remainder theorem and taylor expansion but I can't figure out where we got the LHS and RHS from and the proper method behind it.
$$\frac{3x^2}{2} < \frac{1}{ \sqrt{2x+1}}-1+x+ \frac{5x^3}{2} < \frac{3x^2}{2}+ \frac{35x^4}{8}$$