Question

Solve the system of inequalities: |3-9a| less than or equal to 60

Answer 1

$|3-9a|\leq60\iff3-9a\leq60\ \wedge\ 3-9a\geq-60\qquad|-3\\\\-9a\leq57\ \wedge\ -9a\geq-63\qquad|\text{change the signs}\\\\9a\geq-57\ \wedge\ 9a\leq63\qquad|:9\\\\a\geq-\dfrac{57}{9}\ \wedge\ a\leq7\\\\a\geq-\dfrac{19}{3}\ \wedge\ a\leq7\to a\in\left[-\dfrac{19}{3},\ 7\right]$