Solve the inequality and graph the solution.

Question

3(v+2)<9
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 $3(v+2)<9$, we start by simplifying it.

1. First, distribute the 3: $$3v+6<9$$

2. Next, subtract 6 from both sides: $$3v<3$$

3. Divide both sides by 3: $$v<1$$

Now, we have the solution $v<1$. This means that $v$ can take any value less than 1.

Graph the Solution

To graph the solution:

1. Endpoints: The endpoint here is 1.
2. Since the inequality is $v<1$ (not $\le$), we use an open circle at 1 to indicate that 1 is not included in the solution.
3. The line or ray will extend to the left of 1, indicating all values less than 1.

Representation of the Graph

• Draw a number line.
• Place an open circle at the point 1.
• Shade the line to the left of 1, indicating all numbers less than 1.

The final graph visually represents the solution $v<1$ with the appropriate open endpoint and shaded area.