Match the inequality to its graph. A. B. C. D. Question 4y + 3 ≤ y + 6 (1 point) Responses A A B B C C D
The correct answer is A.
To match the inequality to its graph, we need to solve the inequality and plot the solution on a graph.
Taking the given inequality:
4y + 3 ≤ y + 6
Subtract y from both sides of the inequality:
3y + 3 ≤ 6
Then subtract 3 from both sides of the inequality:
3y ≤ 3
Next, divide both sides of the inequality by 3:
y ≤ 1
This inequality represents all values of y less than or equal to 1. On a number line, we can represent it as a shaded line from negative infinity to 1, including the point 1.
Now, let's match this graph to the options provided:
A. Graph A: This graph does not represent the inequality y ≤ 1.
B. Graph B: This graph represents the inequality y ≤ 1.
C. Graph C: This graph does not represent the inequality y ≤ 1.
D. Graph D: This graph represents the inequality y ≤ 1.
Therefore, the correct match for the inequality 4y + 3 ≤ y + 6 is B.
To match the inequality to its graph, we need to solve the inequality and analyze its graph.
Given inequality: 4y + 3 ≤ y + 6
To solve the inequality, we will isolate the variable, y:
4y + 3 ≤ y + 6
Subtract y from both sides:
4y - y + 3 ≤ 6
3y + 3 ≤ 6
Subtract 3 from both sides:
3y ≤ 3
Divide by 3:
y ≤ 1
So, the solution to the inequality is y ≤ 1.
Now, let's analyze the options:
A. Graph A: Let's substitute y = 1 into the inequality: 4(1) + 3 ≤ (1) + 6. This simplifies to 7 ≤ 7, which is true. Therefore, graph A is a solution to the inequality y ≤ 1.
B. Graph B: Let's substitute y = 1 into the inequality: 4(1) + 3 ≤ (1) + 6. This simplifies to 7 ≤ 7, which is true. Therefore, graph B is also a solution to the inequality y ≤ 1.
C. Graph C: Let's substitute y = 1 into the inequality: 4(1) + 3 ≤ (1) + 6. This simplifies to 7 ≤ 7, which is true. Therefore, graph C is also a solution to the inequality y ≤ 1.
D. Graph D: Let's substitute y = 1 into the inequality: 4(1) + 3 ≤ (1) + 6. This simplifies to 7 ≤ 7, which is true. Therefore, graph D is also a solution to the inequality y ≤ 1.
So, the answer is D: Graph D.