Choose the correct solution and graph for the inequality. -y/2≤3 (1 point) y≤6 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. Image with alt text: y greater-than-or-equal-to 6 Image with alt text: A number line has a closed circle at 6 and is filled in to the right. Skip to navigation
The correct solution and graph for the inequality -y/2 ≤ 3 is: y ≤ 6.
The correct graph is: Image with alt text: A number line has a closed circle at 6 and is filled in to the left.
The correct solution and graph for the inequality -y/2≤3 is:
y≥-6
The correct graph is:
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. Here's the step-by-step process:
Step 1: Multiply both sides of the inequality by -2. Remember, when you multiply or divide an inequality by a negative number, the direction of the inequality sign flips.
(-y/2) * -2 ≥ 3 * -2
This simplifies to:
y ≥ -6
So, the correct solution to the inequality is y ≥ -6.
Now let's graph this on a number line.
Draw a number line and mark -6 on it. Since the inequality is "greater than or equal to," we will include -6 in the solution. Place a closed circle at -6.
Since the inequality is y ≥ -6, we fill in the number line to the right of -6, indicating that any value greater than or equal to -6 satisfies the inequality.
The correct graph for the inequality y ≥ -6 will have a closed circle at -6 and be filled in to the right.