The inequalities should be matched with the graphs that represent them as follows;
6. 4y + 3 ≤ y + 6 ↔ graph C.
7. -2y > 2 ↔ graph A.
8. y/3 < -1 ↔ graph D.
9. 3y ≤ 2y + 3 ↔ graph B.
Based on the information provided, we would determine the solution set for each of the given inequality by simplifying as follows;
4y + 3 ≤ y + 6
By rearranging and collecting like terms, we have the following;
4y - y ≤ 6 - 3
3y ≤ 3
By dividing both sides of the inequality by 3, we have;
y ≤ 1 (solid dot at point 1 and it decreases to the left).
Part 7.
-2y > 2
By dividing both sides of the inequality by -2, we would flip (reverse) the inequality symbol;
-2y/-2 > 2/-2
y < -1 (hollow dot at point -1 and it decreases to the left).
Part 8.
y/3 < -1
By cross-multiplying, we have;
y < -3 (hollow dot at point -3 and it decreases to the left).
Part 9.
3y ≤ 2y + 3
By rearranging and collecting like terms, we have the following;
3y - 2y ≤ 3
y ≤ 3 (solid dot at point 3 and it decreases to the left).