Matching
Match the inequality to its graph.
A. A number line is labeled from negative 5 to 1. There is an open circle on negative 1 and the line is shaded to the left.
B. A number line is labeled from negative 3 to 4. There is a closed circle on 3 and the line is shaded to the left.
C. A number line is labeled from negative 4 to 3. There is a closed circle on 1 and the line is shaded to the left.
D. A number line is labeled from negative 6 to 1. There is an open circle on negative 3 and the line is shaded to the left.
Question
3y ≤ 2y + 3
(1 point)
Responses
A
A
B
B
C
C
D
D
B
To match the inequality to its graph, we need to solve the inequality first:
3y ≤ 2y + 3
To solve for y, we'll subtract 2y from both sides:
y ≤ 3
This means that y is less than or equal to 3.
Now let's match this inequality to its graph:
The correct match for the inequality 3y ≤ 2y + 3 is:
C. A number line is labeled from negative 4 to 3. There is a closed circle on 1 and the line is shaded to the left.
To determine which inequality matches the given descriptions, we can solve the inequality and analyze the solution.
Given inequality: 3y ≤ 2y + 3
To solve this inequality, we need to isolate the variable y on one side of the inequality symbol.
3y - 2y ≤ 2y - 2y + 3 (subtracting 2y from both sides to isolate y)
y ≤ 3
Now that we have the solution y ≤ 3, we can analyze the given descriptions and match it with the correct inequality and graph.
A. "A number line is labeled from negative 5 to 1. There is an open circle on negative 1 and the line is shaded to the left."
This does not match the solution y ≤ 3, so we can eliminate option A.
B. "A number line is labeled from negative 3 to 4. There is a closed circle on 3 and the line is shaded to the left."
This matches the solution y ≤ 3, as the number line is labeled from negative 3 to 4, and there is a closed circle on 3 (which means it includes 3) and the line is shaded to the left. Therefore, we can consider option B as a potential match.
C. "A number line is labeled from negative 4 to 3. There is a closed circle on 1 and the line is shaded to the left."
This does not match the solution y ≤ 3, so we can eliminate option C.
D. "A number line is labeled from negative 6 to 1. There is an open circle on negative 3 and the line is shaded to the left."
This does not match the solution y ≤ 3 either, so we can eliminate option D.
Therefore, the correct match for the inequality 3y ≤ 2y + 3 is option B.