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  • 23-10-2018
  • Mathematics
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Solve the system of inequalities: |3-9a| less than or equal to 60

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gmany
gmany gmany
  • 23-10-2018

[tex]|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][/tex]

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