Which of these inequalities best represents this situation?
Write an inequality to represent the number of bags of popcorn sold, [math]p[/math], and the number of cups of lemonade sold, [math]c[/math], in order to make a profit.
Explain how we could check if the boundary is included or excluded from the solution region.
[size=150]An after-school program has a budget of $200 for a trip to the aquarium.[/size][br][br]If the boundary line in each graph represents the equation [math]11x+6y=200[/math], which graph represents the cost constraint in this situation?
[size=150]The club member receiving the jar asked, "Do you happen to know how much is in the jar?" Tyler said, "I know it's at least $8.50, but I don't know the exact amount."[/size][br][br]Write an inequality to represent the relationship between the number of dimes, [math]d[/math], the number of quarters, [math]q[/math], and the dollar amount of the money in the jar.[br]
Explain what a solution means in this situation.
Suppose Tyler knew there are 25 dimes in the jar. Write an inequality that represents how many quarters could be in the jar.[br]
[size=150][math]14x+3\le8x+3[/math][br]He first solves a related equation.[/size][br][br][math]\displaystyle \begin{align} 14x + 3 = 8x + 3 \\ 14x = 8x \\ 8 = 14 \end{align}[/math][br][br]This seems strange to Andre. He thinks he probably made a mistake. What was his mistake?
Write a system of equations to describe the relationships between the quantities in Kiran's statement. Be sure to specify what each variable represents.[br]
Elena says, “That can't be right.” Explain how Elena can tell that something is wrong with Kiran's statement.
Kiran says, “Oops, I meant to say I bought 2.25 pounds of lentils.” Revise your system of equations to reflect this correction.[br]
Is it possible to tell for sure how many pounds of each kind of lentil Kiran might have bought? Explain your reasoning.[br]
[math]-7-\left(3x+2\right)<-8\left(x+1\right)[/math][br][br]Select [b]all [/b]the values of [math]x[/math] that are solutions to the inequality.
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[/img][br][br]Are the points [math]\left(1.5,-4\right)[/math] and [math]\left(0,-4\right)[/math] solutions to the equation? Explain or show how you know.[br]
Check if each of these points is a solution to the inequality [math]6x+2y\le-8[/math]:[br][list][*][math](\text{-}2,2)[/math][/*][/list]
[list][*][math](4,\text{-}2)[/math][/*][/list]
[list][*][math](0,0)[/math][/*][/list]
[list][*][math](\text{-}4,\text{-}4)[/math][/*][/list]
Are the points on the line included in the solution region? Explain how you know.[br]