C. negative five-sevenths is less than or equal to x is less than or equal to 1
1) Let's solve this inequality and then consider the options:
[tex]\begin{gathered} 7x^2-2x\le \:5 \\ \\ 7x^2-2x-5\le \:5-5 \\ \\ 7x^2-2x-5\le\:0\:\:\:Factor\:this: \\ \\ \left(7x^2+5x\right)+\left(-7x-5\right)\leq0 \\ \\ x\left(7x+5\right)-\left(7x+5\right)\leq0 \\ \\ \left(7x+5\right)\left(x-1\right)\leq0 \\ \\ x=-\frac{5}{7}\quad \mathrm{or}\quad \:-\frac{5}{7}Thus, as we can see the only possible answer is
C, since that presents the restraints we have found algebraically.