Choose the correct solution and graph for the inequality.
(3y-6)/3+4≤-2 or (4y-8)/2-1≥5

(1 point)
Responses


At negative 4, is a filled in circle. The number line is shaded to the left of negative 4. Halfway between positive 4 and positive 6, is a filled in circle. The number line is shaded to the right of the filled in circle.
Image with alt text: y is less than or equal to negative 4 or y is greater than or equal to 5 Image with alt text: A number line has a closed circle at negative 4 and is filled in to the left and another closed circle at 5 and is filled in to the right. At negative 4, is a filled in circle. The number line is shaded to the left of negative 4. Halfway between positive 4 and positive 6, is a filled in circle. The number line is shaded to the right of the filled in circle.



Image with alt text: y is less than or equal to 6 or y is greater than or equal to negative 5 Image with alt text: A number line has a closed circle at negative 5 and is filled in to the right and another closed circle at 6 and is filled in to the left.


Halfway between negative 6 and negative 4, is a filled in circle. The number line is shaded to the left of the filled in circle. Halfway between positive 4 and positive 6, is a filled in circle. The number line is shaded to the right of the filled in circle.
Image with alt text: y is less than or equal to negative 5 or y is greater than or equal to 5 Image with alt text: A number line has a closed circle at negative 5 and is filled in to the left and another closed circle at 5 and is filled in to the right. Halfway between negative 6 and negative 4, is a filled in circle. The number line is shaded to the left of the filled in circle. Halfway between positive 4 and positive 6, is a filled in circle. The number line is shaded to the right of the filled in circle.



The correct solution and graph for the inequality are:
A number line has a closed circle at -4 and is filled in to the left, and another closed circle at 5 and is filled in to the right. The number line is shaded to the left of -4 and to the right of 5.
The correct response is:
Image with alt text: y is less than or equal to -4 or y is greater than or equal to 5
The correct solution and graph for the inequality is:
"At negative 4, there is a filled-in circle. The number line is shaded to the left of negative 4. Halfway between positive 4 and positive 6, there is a filled-in circle. The number line is shaded to the right of the filled-in circle."
Image with alt text: y is less than or equal to -4 or y is greater than or equal to 5
Image with alt text: A number line has a closed circle at -4 and is filled in to the left and another closed circle at 5 and is filled in to the right.
To solve the inequality (3y-6)/3+4≤-2, we need to perform the following steps:
Step 1: Simplify the expression on the left side of the inequality.
Start by multiplying both sides of the equation by 3 to eliminate the fraction:
3 * [(3y-6)/3 + 4] ≤ -2 * 3
Simplifying further:
(3y-6) + 12 ≤ -6
3y + 6 ≤ -6
Subtract 6 from both sides:
3y ≤ -12
Divide by 3:
y ≤ -4
So, the solution to the first part of the inequality is y ≤ -4.
To solve the inequality (4y-8)/2-1≥5, we follow the same steps:
Step 1: Simplify the expression on the left side of the inequality.
Start by multiplying both sides of the equation by 2 to eliminate the fraction:
2 * [(4y-8)/2 - 1] ≥ 5 * 2
Simplifying further:
(4y-8) - 2 ≥ 10
4y - 8 - 2 ≥ 10
4y - 10 ≥ 10
Add 10 to both sides:
4y ≥ 20
Divide by 4:
y ≥ 5
So, the solution to the second part of the inequality is y ≥ 5.
Next, we need to combine the solutions for both parts of the inequality.
The first solution is y ≤ -4. This means that y can be any value less than or equal to -4.
The second solution is y ≥ 5. This means that y can be any value greater than or equal to 5.
To graph the solution on a number line, we can represent the values between -4 and 5 as a shaded region. We include closed circles at -4 and 5 to indicate that these points are included in the solution.
So, the correct solution and graph for the inequality is:
y is less than or equal to -4 or y is greater than or equal to 5.
On the number line, we have a closed circle at -4 and it is filled in to the left. We also have a closed circle at 5 and it is filled in to the right. The shaded region is to the left of -4 and to the right of 5.