Solving Inequalities: math test solutions, Grade 7 – download the PDF

1 Symbols and values / 4 pts

1. \(n \le 15\). (1 pt)
2. False: \(-7\) is to the right of \(-9\), so \(-7 \gt -9\). (1 pt)
3. \(2(3) + 1 = 7\) and \(7 \ge 7\) is true, so yes. (1 pt)
4. \(4 - (-2) = 6\) and \(6 \lt 5\) is false, so no. (1 pt)

2 Solve and graph / 4 pts

(a) \(4x \lt 20\), so \(x \lt 5\) (1 pt). Open circle at 5, shade left (1 pt).

(b) Subtract 4: \(-3x \ge 15\). Divide by \(-3\) and flip: \(x \le -5\) (1 pt). Closed circle at \(-5\), shade left (1 pt).

3 Negative coefficient with a fraction / 3 pts

Subtract 6: \(-\dfrac{x}{3} \le -4\) (1 pt). Multiply by \(-3\) and flip the sign: \(x \ge 12\) (1 pt). Check: \(x = 15\) gives \(6 - 5 = 1 \le 2\), true (1 pt).

4 Gym membership / 4 pts

Total cost \(20 + 18m\); at most 200: \(20 + 18m \le 200\) (1 pt). Subtract 20: \(18m \le 180\) (1 pt). Divide by 18: \(m \le 10\) (1 pt). Sam can stay a member for at most 10 months, which costs exactly 200 dollars (1 pt).

5 Error analysis / 3 pts

She divided by \(-5\) but did not reverse the sign (1 pt). Correct: \(x \gt -7\) (1 pt). Check with \(x = 0\): \(0 \lt 35\) is true, whereas \(x = -10\) gives \(50 \lt 35\), false (1 pt).

6 Whole-number solutions / 2 pts

\(3x \lt 16\), so \(x \lt 5.33\ldots\) (1 pt). With \(x \ge 2\), the whole numbers are 2, 3, 4, 5 (1 pt).