5 exercises · 2 automatically checked · 3 written self-checks · Untimed
2 questions · Shuffled order · Untimed practice
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A purchase costs 12 + 4.5n dollars, with integer n ≥ 0. For a $50 budget, find the greatest n.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
8. The budget gives 4.5n ≤ 38, so n ≤ 76/9, between 8 and 9. Eight items cost $48; nine cost $52.50. Only 8 is the greatest permitted integer.
If y ≥ x + 2 and y ≤ −2x + 11, find the greatest real x.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
3. An allowed y requires x + 2 ≤ −2x + 11, so 3x ≤ 9 and x ≤ 3. At x
Write your complete response before opening the model answer. Compare both your answer and your reasoning.
Solve 9 − 4x ≥ 1.
x ≤ 2. Subtract 9: −4x ≥ −8. Division by −4 reverses the comparison and gives x ≤ 2. The endpoint satisfies the original inequality with equality.
Solve −2 < 3x + 1 ≤ 10.
−1 < x ≤ 3. Subtract 1 from every part to get −3 < 3x ≤ 9, then divide by 3. The lower endpoint is excluded; the upper endpoint is included.
Does (2, 3) satisfy x + 2y < 8? Explain the boundary issue.
No. The left side at (2, 3) is 2 + 2(3)