Choose the correct solution and graph for the inequality.
-y/2≤3

(1 point)
Responses



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



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



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



The correct solution and graph for the inequality -y/2≤3 is:
Image with alt text: y greater-than-or-equal-to negative 6
Image with alt text: A number line has a closed circle at negative 6 and is filled in to the right.
The correct solution and graph for the inequality -y/2 ≤ 3 is:
Image with alt text: y greater-than-or-equal-to negative 6
Image with alt text: A number line has a closed circle at negative 6 and is filled in to the right.
To solve the inequality -y/2 ≤ 3, we need to isolate the variable y by performing the necessary steps:
1. Multiply both sides of the inequality by 2 to eliminate the fraction: -(y/2) * 2 ≤ 3 * 2, which simplifies to -y ≤ 6.
2. To isolate y, we need to multiply both sides of the inequality by -1. Remember, when multiplying or dividing by a negative number, we need to reverse the inequality sign. So, we have -y * (-1) ≥ 6 * (-1), which becomes y ≥ -6.
Therefore, the correct solution to the inequality is y ≥ -6.
Now let's graph this inequality on a number line:
1. Draw a number line.
2. Represent -6 on the number line with a closed circle (to indicate that it is included in the solution set).
3. Shade the number line to the right of the closed circle (to represent y values greater than or equal to -6).
So, the correct graph for the inequality -y/2 ≤ 3 is:
Image with alt text: y greater-than-or-equal-to negative 6
Image with alt text: A number line has a closed circle at negative 6 and is filled in to the right.