The structure functions $F_2^{\rm ep}$ and $F_2^{\rm en}$ for electron-proton and electron-neutron deep inelastic scattering deduced from the model of valence quarks and sea quarks of proton and neutron have the expressions$$
\frac{1}{x}F_2^{\rm ep}(x)=\Big(\frac{2}{3}\Big)^2[u_p(x)+\bar{u}_p(x)]
+\Big(\frac{1}{3}\Big)^2[d_p(x)+\bar{d}_p(x)]
+\Big(\frac{1}{3}\Big)^2[s_p(x)+\bar{s}_p(x)],\\
\frac{1}{x}F_2^{\rm en}(x)=\Big(\frac{2}{3}\Big)^2[u_n(x)+\bar{u}_n(x)]
+\Big(\frac{1}{3}\Big)^2[d_n(x)+\bar{d}_n(x)]
+\Big(\frac{1}{3}\Big)^2[s_n(x)+\bar{s}_n(x)]$$ where $u_p, d_p, s_p$ are the momentum distribution functions $f_i(x)$ for $u, d$ and $s$ quarks while $\bar{u}_p, \bar{d}_p, \bar{s}_p$ are those of $\bar{u},\bar{d}$ and $\bar{s}$ antiquarks inside the proton, respectively. If isospin symmetry is considered to be exact (very small violation), the $u$-qurks distribution in proton should be same as the $d$ quarks distribution in th neutron and vice-versa. Also, the s-quarks and $\bar{s}$-antiquarks distributions will be same in the proton and the neutron. Therefore, $$
u_p(x) =d_n(x)\equiv u(x), ~~ d_p(x) =u_n(x)\equiv d(x),~~s_p(x) =s_n(x) \equiv s(x).$$ With this simplification, the expressions for the structure cosntants become, $$
\frac{1}{x}F_2^{\rm ep}(x) = \Big(\frac{2}{3}\Big)^2[u(x)+\bar{u}_p(x)]
+\Big(\frac{1}{3}\Big)^2[d(x)+\bar{d}_p(x)]
+\Big(\frac{1}{3}\Big)^2[s(x)+\bar{s}(x)],\\
\frac{1}{x}F_2^{\rm en}(x) = \Big(\frac{2}{3}\Big)^2[d(x)+\bar{u}_n(x)]
+\Big(\frac{1}{3}\Big)^2[u(x)+\bar{d}_n(x)]
+\Big(\frac{1}{3}\Big)^2[s(x)+\bar{s}(x)].$$ Using $$u(x)=u_v(x)+u_{\rm sea}(x), d(x)=d_v(x)+d_{\rm sea}(x)$$ and realising that for other quarks and antiquarks, the contribution entirely come from sea quarks, one finally ends up getting $$
\frac{1}{x}F_2^{\rm ep}(x) = \Big(\frac{1}{9}\Big)[4u_v+d_v]
+\Big(\frac{4}{3}\Big)S(x), \\
\frac{1}{x}F_2^{\rm en}(x) =  \Big(\frac{1}{9}\Big)[u_v+4d_v]
+\Big(\frac{4}{3}\Big)S(x).$$

In an exercise of Halzen and Martin's Particle Physics text, they've asked to show that $$\frac{1}{4}\leq\frac{F_2^{\rm en}}{F_2^{\rm ep}}\leq 4.$$ They say that this is obvious but I cannot prove this result. Any help will be very much appreciated.