Question

solve the inequality and graph the solution.
f + 11 ≤ 19
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: Isolate the variable \( f \)

Subtract \( 11 \) from both sides of the inequality \( f + 11\leq19 \).
Using the subtraction property of inequalities \( f+11 - 11\leq19 - 11 \).

Step2: Simplify the inequality

Simplify the left - hand side \( f+11 - 11=f \) and the right - hand side \( 19 - 11 = 8 \). So, \( f\leq8 \).

To graph \( f\leq8 \):

• Plot a closed endpoint at \( 8 \) (because the inequality is \( \leq \), which includes the value \( 8 \)).
• Draw a ray to the left (since \( f \) is less than or equal to \( 8 \)).

Answer:

The solution of the inequality \( f + 11\leq19 \) is \( f\leq8 \). On the number line, there is a closed circle at \( 8 \) and a ray extending to the left.