Question

solve the inequality and graph the solution.
w - 6 ≤ 3
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.

Explanation:

Step1: Add 6 to both sides

To solve the inequality \( w - 6 \leq 3 \), we add 6 to both sides of the inequality. This is based on the addition property of inequalities, which states that if we add the same number to both sides of an inequality, the inequality sign remains the same.

$$ w - 6 + 6 \leq 3 + 6 $$

Step2: Simplify both sides

Simplifying the left - hand side, \( w-6 + 6=w \). Simplifying the right - hand side, \( 3 + 6 = 9 \). So we get \( w\leq9 \).

For graphing the solution:

• The endpoint is at \( w = 9 \) (since the inequality is \( \leq \), the endpoint is a closed circle, indicating that 9 is included in the solution set).
• We draw a ray starting from the point \( w = 9 \) and extending to the left (because we want all values of \( w \) that are less than or equal to 9).

Answer:

The solution to the inequality is \( w\leq9 \). For the graph, plot a closed circle at 9 on the number line and draw a ray pointing to the left.