DOL 5 Part B Review

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Answer explanation

To solve the inequality 4x - y ≥ 8, rearrange it to isolate y: -y ≥ -4x + 8. Multiplying by -1 reverses the inequality, giving y ≤ 4x - 8. Thus, the correct answer is y ≤ 4x - 8.

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Answer explanation

To solve the inequality for y, isolate y by subtracting 3x from both sides: y ≤ 5 - 3x. Thus, the correct answer is y ≤ 5 - 3x.

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A school plans to spend no more than $3,000 to purchase tablets and printers for a classroom. Each tablet costs $200, and each printer costs $100. Which inequality shows all possible combinations of x, the number of tablets, and y, the number of printers, the school can buy?

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Answer explanation

The school wants to spend no more than $3,000. The cost for tablets (x) is $200 each and for printers (y) is $100 each. The correct inequality representing this budget constraint is 200x + 100y ≤ 3,000.

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Nathan wants to become a Youtube gamer. For every view he receives $0.25 (x) and $0.05 for every advertisement (y) that people watch. He must earn at least $3600 every month to pay his bills and meet business expenses. Which inequality best models his business?

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Answer explanation

Nathan earns $0.25 per view (x) and $0.05 per ad (y). To meet his monthly expenses of at least $3600, the correct inequality is 0.25x + 0.05y ≥ 3600, indicating he needs to earn that amount or more.

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B

Answer explanation

The inequality x + 2y ≥ 6 represents a region above the line x + 2y = 6. Graph B correctly shows this shaded area, indicating all points satisfying the inequality, while the other options do not represent the correct region.

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A

Answer explanation

The inequality 3x + y \ge 2 represents a region above the line y = -3x + 2. Graph A correctly shows this shaded area, indicating all points satisfying the inequality, while other options do not represent the correct region.

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Answer explanation

The inequality y > (1/2)x - 4 indicates the region above the line y = (1/2)x - 4. Since the inequality is strict (greater than), the boundary line is dashed, meaning it is not included in the solution set.

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Answer explanation

To solve the inequality 5(x - 3) < 2x + 9, first distribute: 5x - 15 < 2x + 9. Then, subtract 2x from both sides: 3x - 15 < 9. Next, add 15: 3x < 24. Finally, divide by 3: x < 8. Thus, the correct choice is x < 6.

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Answer explanation

To solve the inequality 4(x + 2) > 3x - 5, first distribute: 4x + 8 > 3x - 5. Then, subtract 3x from both sides: x + 8 > -5. Subtract 8: x > -13. Thus, the correct inequality is x > -13.

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How many solutions are shown?

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1

Answer explanation

The question asks for the number of solutions shown. The correct answer is 1, indicating there is exactly one solution presented.