Question 1: Solve and graph (2 points)
Subtract 4: \(3x>15\). Divide by 3: \(x>5\). Open circle at 5, shade right.
Scoring: 1 point for \(x>5\); 1 point for a correct graph with an open circle.
Question 2: Negative coefficient (2 points)
Add 3: \(-5x\le 15\). Divide by \(-5\) and reverse the sign: \(x\ge -3\). Closed circle at \(-3\), shade right.
Scoring: 1 point for \(x\ge -3\) (including the reversed sign); 1 point for a correct graph with a closed circle.
Question 3: Testing values (2 points)
The inequality is \(4x< 12\), so \(x< 3\).
(a) \(4(2)-7=1< 5\): yes.
(b) \(4(3)-7=5< 5\) is false: no.
Scoring: 1 point for each correct decision with a substitution shown.
Question 4: Find the error (2 points)
Ethan divided both sides by \(-4\) but did not reverse the inequality sign. The correct solution is \(x<-4\).
Scoring: 1 point for naming the missing sign reversal; 1 point for \(x<-4\).
Question 5: Fraction coefficient (2 points)
Add 3: \(\frac{x}{4}\ge 5\). Multiply by 4: \(x\ge 20\).
Scoring: 1 point for \(\frac{x}{4}\ge 5\); 1 point for \(x\ge 20\).
Question 6: Reading a graph (2 points)
(a) A closed circle at 3 with shading to the right: \(x\ge 3\).
(b) \(2x\ge 6\), so \(2x+1\ge 7\). The blank is 7.
Scoring: 1 point for each part.
Question 7: Saving for a skateboard (3 points)
(a) \(40+6w>100\).
(b) \(6w>60\), so \(w>10\).
(c) \(w\) must be more than 10, so the fewest whole number is 11 weeks (at 10 weeks he has exactly \(\$100\)).
Scoring: 1 point per part.
Question 8: Freezer cooling (3 points)
(a) \(8-4h<-12\).
(b) \(-4h<-20\). Divide by \(-4\) and reverse the sign: \(h>5\).
(c) The freezer is below \(-12^{\circ}\text{F}\) after more than 5 hours (it is exactly \(-12^{\circ}\text{F}\) at 5 hours).
Scoring: 1 point per part; part (b) needs the reversed sign.
Question 9: Solve with a leading constant (2 points)
Subtract 7: \(-2x\ge 8\). Divide by \(-2\) and reverse the sign: \(x\le -4\).
Scoring: 1 point for \(-2x\ge 8\); 1 point for \(x\le -4\).
20 points
See every chapter on the Grade 7 math page.