Question

for which values of A the system has at least one solution$x \leqslant 7 \\ x \geqslant a$

Answer 1

The system has at least a solution when

$a\leq\text{ 7}$

Since

$\begin{gathered} x\text{ }\leq\text{ 7 and x }\ge\text{ a} \\ \text{This implies that } \\ x\text{ }\leq\text{ 7 and a}\leq\text{ x} \\ \text{Hence, we can say that} \\ a\text{ }\leq\text{ x}\leq\text{ 7} \\ Thus,\text{ a can take any value but not exceeding 7} \end{gathered}$