Question

This graph shows some solutions to 5x + 9y < 45

Answer 1

solutions to an inequality are pairs that make the inequality true, or namely lie in the shaded or true region.

`(1,1)\hspace{5em}5(1)+9(1) < 45\implies 14 < 45\qquad \textit{is this true?} ~~ \textit{\LARGE \checkmark} \\\\\\ (4,0)\hspace{5em}5(4)+9(0) < 45\implies 20 < 45\qquad \textit{is this true?} ~~ \textit{\LARGE \checkmark}`

`(10,4)\hspace{4em}5(10)+9(4) < 45\implies 86 < 45\qquad \textit{is this true?} ~~ \bigotimes \\\\\\ (0,10)\hspace{4em}5(0)+9(10) < 45\implies 90 < 45\qquad \textit{is this true?} ~~\bigotimes \\\\\\ (6,-1)\hspace{4em}5(6)+9(-1) < 45\implies 21 < 45\qquad \textit{is this true?} ~~\textit{\LARGE \checkmark}`