Solve for in. 3x-8leqslant 23 AND -4x+26geqslant 6 Choose 1 answer: (A) A xleqslant (31)/(3) B xleqslant 5 C 5leqslant xleqslant (31)/(3) D There are no solutions E All values of a are solutions

To solve the system of inequalities, we need to solve each inequality separately and then find the intersection of the solutions.<br /><br />For the first inequality, $3x-8\leqslant 23$, we can add 8 to both sides to get $3x\leqslant 31$. Dividing both sides by 3, we get $x\leqslant \frac{31}{3}$.<br /><br />For the second inequality, $-4x+26\geqslant 6$, we can subtract 26 from both sides to get $-4x\geqslant -20$. Dividing both sides by -4 (and reversing the inequality sign since we divided by a negative number), we get $x\leqslant 5$.<br /><br />Therefore, the solution to the system of inequalities is $x\leqslant 5$, which corresponds to option B.