Question

solve the inequality and graph the solution.

$w - 19 \leq - 16$

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.

Explanation:

Step1: Isolate the variable \( w \)

Add \( 19 \) to both sides of the inequality \( w - 19\leq - 16 \).
$$w-19 + 19\leq -16+19$$

Step2: Simplify the inequality

Simplify the left - hand side \( w-19 + 19=w \) and the right - hand side \( -16 + 19 = 3 \). So, \( w\leq3 \).

To graph \( w\leq3 \):

• The endpoint is at \( w = 3 \). Since the inequality is \( \leq \) (less than or equal to), the endpoint at \( 3 \) is closed (a filled - in circle).
• The solution set includes all real numbers less than or equal to \( 3 \), so we draw a ray to the left of \( 3 \) on the number line.

Answer:

The solution of the inequality \( w-19\leq - 16 \) is \( w\leq3 \). On the number line, we have a closed circle at \( 3 \) and a ray extending to the left.