Question

1. solve the compound inequality and graph the solution set f - 6 < 5 and f - 4 ≥ 2

Explanation:

Step1: Solve first inequality

Add 6 to both sides:
$f - 6 + 6 < 5 + 6$
$f < 11$

Step2: Solve second inequality

Add 4 to both sides:
$f - 4 + 4 \geq 2 + 4$
$f \geq 6$

Step3: Combine the solutions

Since it's an "and" compound inequality, we take the overlap of the two solution sets.
$6 \leq f < 11$

Step4: Graph description

On a number line:

• Draw a closed circle at 6 (since $f \geq 6$ includes 6)
• Draw an open circle at 11 (since $f < 11$ does not include 11)
• Shade the region between 6 and 11.

Answer:

The solution set is $6 \leq f < 11$.
For the graph: A number line with a closed dot at 6, an open dot at 11, and the segment between them shaded.