Write and solve inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r }$$ or $${p(x+q)<r.}$$
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In this lesson, students will solve inequalities in which the coefficient of the variable is positive. Multiplying and dividing with negative values in inequalities will be addressed in Lesson 10.
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On Saturday, Bianca has $50 on her debit card when she goes out with some friends. She uses her debit card to spend $14.50 on lunch. She and her friends would like to go to see a movie, but some of her friends are out of money. If the movie tickets cost $6.50 each, how many tickets can Bianca buy without overdrawing on her debit card?
Identical copies of books are being packaged and shipped to a bookstore. There are 18 boxes of books that each weigh 31 pounds. The boxes have space for some more books to be added; however, the total weight of all of the boxes cannot exceed 615 pounds. Two workers, Kevin and Olivia, want to determine how many more pounds of books they can add into each box without going over the weight limit.
Kevin writes the inequality $${18(x+31)\geq 615}$$.
Olivia writes the inequality $${18(x+31)\leq 615}$$.
Who wrote the correct inequality? How many extra pounds can they add to each box?
Solve and graph the solution to each inequality below.
a. $${{2\over3} (x-15)>-24}$$
b. $${-1.6+3x \leq 8}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.
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Grace has $105 to buy a cake and pizza for her cousin’s birthday party. She knows she needs to set aside $25 for the cake, and the rest of the money she can spend on pizzas. Each pizza costs $9.25. How many pizzas can Grace afford to buy?
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