Hey guys! I need help with this question ASAP! Thank you so much for anyone that helps!
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.
4y + 3 ≤ y + 6
A. A
B. B
C. C
D. D
This is due tomorrow, so if anyone could lend a hand, I would be full of thanks. Tysm!
-Lupa
I believe that the best answer choice would be C. If you work out the inequality, (4y + 3 less than or equal to y + 6) you are left with y = 1. Since the sign used in this inequality is less than or equal to, you would mark the starting point at positive 1 and go to the left with a closed circle. Hence, C matches this result. Hope this helps you out :D
Oh! Tysm for responding so quickly! And tysm for your help! Got it correct!
Sure thing, Lupa! I'm here to help you out with a bit of humor. So, let's figure out which inequality matches its graph.
Now, let's take a closer look at the inequality: 4y + 3 ≤ y + 6.
To determine the answer, we need to isolate "y" on one side of the inequality. Let's subtract "y" from both sides:
4y - y + 3 ≤ y - y + 6.
Simplifying this equation, we get:
3y + 3 ≤ 6.
Next, we can subtract 3 from both sides:
3y + 3 - 3 ≤ 6 - 3.
This simplifies to:
3y ≤ 3.
Lastly, we need to divide both sides by 3:
3y/3 ≤ 3/3.
Which simplifies to:
y ≤ 1.
So, the correct answer is option A, which describes a number line labeled from negative 5 to 1, with an open circle on negative 1, and the line shaded to the left.
To match the inequality to its graph, let's analyze the given inequality:
4y + 3 ≤ y + 6
To solve this inequality, we need to isolate the variable "y" on one side of the inequality sign. Here are the steps:
1. Start by subtracting "y" from both sides of the inequality to get rid of the "y" term on the right side:
4y - y + 3 ≤ y - y + 6
This simplifies to:
3y + 3 ≤ 6
2. Next, subtract 3 from both sides of the inequality to isolate the "y" term:
3y + 3 - 3 ≤ 6 - 3
This simplifies to:
3y ≤ 3
3. Finally, divide both sides of the inequality by 3 to solve for "y":
(3y) / 3 ≤ 3 / 3
This simplifies to:
y ≤ 1
Now that we have solved the inequality, we can match it to its graph. Let's analyze each option:
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.
The correct answer is C.
This is because the graph matches the inequality y ≤ 1. The closed circle on 1 represents that 1 is included in the solution, and the shading to the left indicates that all values less than or equal to 1 satisfy the inequality.
Therefore, the correct match for the given inequality is:
4y + 3 ≤ y + 6 ===> Option C
To solve this question, we need to rearrange the given inequality and then compare it with the options one by one.
The given inequality is: 4y + 3 ≤ y + 6
To solve it, we start by isolating the variable y. We can do this by subtracting y from both sides:
4y - y + 3 ≤ y - y + 6
3y + 3 ≤ 6
Next, we subtract 3 from both sides to isolate the term with y:
3y ≤ 6 - 3
3y ≤ 3
Lastly, we divide both sides by 3 to solve for y:
(3y)/3 ≤ 3/3
y ≤ 1
Now that we have simplified the inequality, we need to match it with the correct graph. Let's compare each option:
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.
The open circle on -1 suggests that y is not included in the solution, but our inequality states y ≤ 1. Therefore, option A does not match our inequality.
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.
The closed circle on 3 indicates that y = 3 is included in the solution, but our inequality states y ≤ 1. Therefore, option B does not match our inequality.
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.
The closed circle on 1 suggests that y = 1 is included in the solution, and our inequality states y ≤ 1. Therefore, option C matches our inequality.
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.
The open circle on -3 suggests that y is not included in the solution, but our inequality states y ≤ 1. Therefore, option D does not match our inequality.
Therefore, the correct match for the inequality 4y + 3 ≤ y + 6 is option C, which is graph C.
I hope this explanation helps! Let me know if you have any further questions.