Choose the correct solution and graph for the inequality.
- y/2 ≤3
The correct solution for the inequality -y/2 ≤ 3 is y ≥ -6.
To graph this inequality, we draw a solid line going horizontally through -6 on the y-axis, since the inequality includes "greater than or equal to" (-6 is included). Then, we shade the region above the line, as all y-values greater than or equal to -6 satisfy the inequality.
The graph can be shown as:
[graph of the inequality]
To solve the inequality -y/2 ≤ 3, we need to isolate the variable y.
Step 1: Multiply both sides of the inequality by 2: -2 * (-y/2) ≤ 3 * 2.
This simplifies to y ≥ -6.
Step 2: Graph the solution on the number line.
Since y is greater than or equal to -6, we can represent the solution as a closed dot at -6 and an arrow going to the right.
Graph:
---->===============================
-6
In this graph, the shaded region represents the values of y that satisfy the inequality -y/2 ≤ 3.
To solve the inequality, -y/2 ≤ 3, we can follow these steps:
Step 1: Multiply both sides of the inequality by -2 to eliminate the fraction. Remember that when multiplying or dividing by a negative number, we need to reverse the inequality sign.
(-2)(-y/2) ≥ (3)(-2)
This simplifies to:
y ≥ -6
Step 2: Now we have the solution as y ≥ -6. This means that any value of y that is greater than or equal to -6 satisfies the inequality.
To graph the solution on a number line:
1. Draw a number line and mark the point -6 on it.
2. Since the inequality states "greater than or equal to," we put a solid dot at -6 to include this value in the solution.
3. Draw an arrow extending to the right, indicating that the solution continues indefinitely in that direction.
The final graph will show a solid dot at -6 with an arrow going to the right.