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Inequalities: PracticeQuestion 3 of 8Select the correct answer.Carl, Caitlyn, and Daryl are comparing their ages. Carl is two years older than Caitlyn. Daryl is five years older than Carl. The product ofCarl and Daryl's ages is at least 160. If x represents Caitlyn's age, which inequality represents this situation?22 + 141 + 28 > 160O12 +4 > 16012 + 25 + 5 > 160O12 + 9.1 + 14 > 160SubmitReset

Respuesta :

We have the following according the statement (C, age Carl, D age Daryl), X age Caitlyn):

[tex]\begin{gathered} C-2=X \\ D-5=C \\ C\cdot D\leq160 \end{gathered}[/tex]

organizing information:

[tex]\begin{gathered} C=X+2 \\ D=C+5=>D=X+5+2=>D=X+7 \\ (X+2)\cdot(X+7)\leq160 \\ X^2+2X+7X+14\leq160 \\ X^2+9X+14\leq160 \end{gathered}[/tex]

Therefore the answer is: X^2 + 9X +14 <= 160

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