Match the inequality to its graph. A. B. C. D. Question 3y ≤ 2y + 3 (1 point)
A B C D
The inequality 3y ≤ 2y + 3 would be represented by graph A.
To determine the correct graph for the inequality 3y ≤ 2y + 3, we need to solve the inequality and then analyze the solution.
Step 1: Subtract 2y from both sides of the inequality:
3y - 2y ≤ 2y + 3 - 2y
y ≤ 3
Step 2: The solution to the inequality is y ≤ 3, meaning any value of y that is less than or equal to 3 is a solution to the inequality.
Based on this solution, the correct graph should show all the points on or below the line y = 3.
Let's analyze the options to find the correct graph:
A. This graph shows all the points above the line y = 3, so it does not match the inequality 3y ≤ 2y + 3.
B. This graph shows all the points on or below the line y = 3, which matches the inequality 3y ≤ 2y + 3.
C. This graph shows all the points above the line y = 3, so it does not match the inequality 3y ≤ 2y + 3.
D. This graph shows all the points on or below the line y = 3, which matches the inequality 3y ≤ 2y + 3.
Therefore, the correct graph for the inequality 3y ≤ 2y + 3 is option B.
To match the inequality to its graph, we need to first solve the inequality to find its solution set and then determine which graph represents that solution set.
Let's solve the given inequality:
3y ≤ 2y + 3
To isolate the variable, we can subtract 2y from both sides of the inequality:
3y - 2y ≤ 2y + 3 - 2y
y ≤ 3
So, the solution set for the inequality is y ≤ 3.
Now, let's examine the graphs (A, B, C, and D) and find the one that represents the solution set y ≤ 3.
Since I cannot see the graphs, I am unable to provide a specific answer. However, you can use the following tips to determine the correct graph:
1. Look for all the points on the graph that satisfy the inequality y ≤ 3. In other words, find the region where the y-values are less than or equal to 3.
2. Check if the graph includes the line y = 3 or has shading below the line y = 3.
3. Make sure the graph does not include any points where y is greater than 3.
By applying these guidelines, you should be able to match the inequality to its graph by finding the one that represents y ≤ 3.