Solve the inequality and graph the solution.

Question

2v≤6
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \(2v \leq 6\), we start by isolating \(v\).

1. Divide both sides of the inequality by 2: \[ v \leq \frac{6}{2} \] \[ v \leq 3 \]

Now that we have the solution, \(v \leq 3\), we will graph it.

Step 1: Identify the endpoints

• The endpoint is \(v = 3\).

Step 2: Determine whether to use a closed or open dot

Since the inequality is less than or equal to (≤), we will use a closed dot at \(v = 3\) to indicate that this value is included in the solution.

Step 3: Graph the line

• Draw a number line.
• Place a closed dot at \(3\).
• Shade to the left of \(3\) to indicate that all values less than \(3\) are included in the solution.

Summary

The solution to the inequality \(2v \leq 6\) is \(v \leq 3\). The graph will have a closed dot at \(3\) and everything to the left of \(3\) shaded, representing all numbers less than or equal to \(3\).

Here’s a description of how to visualize it:

<---o===========================>
    0  1  2  3  4  5

The "o" is a closed dot at \(3\) and the "=" represents the shaded area (all values less than or equal to \(3\)).