Question

solve the inequality and graph the solution.
4v ≤ 12
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.
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Explanation:

Step1: Isolate the variable \( v \)

To solve the inequality \( 4v \leq 12 \), we divide both sides by 4. Since 4 is a positive number, the direction of the inequality sign remains the same.

$$ \frac{4v}{4} \leq \frac{12}{4} $$

Step2: Simplify both sides

Simplifying the left - hand side gives \( v \), and simplifying the right - hand side gives 3. So we have \( v \leq 3 \).

For graphing the solution:

• The endpoint is at \( v = 3 \). Since the inequality is \( \leq \), the endpoint is a closed circle (because 3 is included in the solution set).
• The arrow of the ray should point to the left (towards negative infinity) to represent all values of \( v \) that are less than or equal to 3.

Answer:

The solution to the inequality is \( v \leq 3 \). To graph it, plot a closed circle at 3 on the number line and draw a ray pointing to the left.