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
4y + 3 ≤ y + 6
(1 point)
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 match the inequality to its graph, let's analyze the given inequality:
4y + 3 ≤ y + 6
To solve this inequality, we can start by isolating the variable y on one side:
4y - y + 3 ≤ 6
Combine like terms:
3y + 3 ≤ 6
Next, we can isolate y by subtracting 3 from both sides:
3y ≤ 6 - 3
3y ≤ 3
Finally, we can divide both sides by the coefficient of y, which is 3:
y ≤ 1
Now that we have solved the inequality, let's match it to the correct graph:
Out of the given options, the correct match for the inequality 4y + 3 ≤ y + 6 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 match the inequality to its graph, we need to simplify the inequality first.
Given inequality: 4y + 3 ≤ y + 6
To begin simplifying the inequality, we can start by getting rid of the terms with y on both sides of the inequality. We can do this by subtracting y from both sides:
4y - y + 3 ≤ y - y + 6
3y + 3 ≤ 6
Next, we want to isolate the variable y. To do this, we can subtract 3 from both sides:
3y + 3 - 3 ≤ 6 - 3
3y ≤ 3
Finally, we can divide both sides of the inequality by 3 to solve for y:
(3y)/3 ≤ 3/3
y ≤ 1
So, the simplified inequality is y ≤ 1.
Now let's match this inequality to one of the given options:
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.
Based on the simplified inequality y ≤ 1, we can see that there is a closed circle on 1, and the line is shaded to the left. Therefore, the matching option is C.