Question

solve the inequality. now test one value less than the boundary, like 5, and one value greater than the boundary, like 7. start with ( f = 5 ). is the inequality statement true or false when ( f = 5 )? (\begin{array}{|c|c|} hline & -4f leq 24 \\ hline f = 5 & square \\ hline f = 6 \text{ (boundary)} & \text{true} \\ hline f = 7 & \\ hline end{array})

Explanation:

Step1: Solve the inequality first

Start with $-4f \leq -24$. Divide both sides by $-4$, remembering to reverse the inequality sign when dividing by a negative number:
$$\frac{-4f}{-4} \geq \frac{-24}{-4}$$
$$f \geq 6$$

Step2: Test $f=5$ in the inequality

Substitute $f=5$ into $-4f \leq -24$:
$$-4(5) = -20$$
Check if $-20 \leq -24$: this is false.

Step3: Test $f=7$ in the inequality

Substitute $f=7$ into $-4f \leq -24$:
$$-4(7) = -28$$
Check if $-28 \leq -24$: this is true.

Answer:

• For $f=5$: false
• Solved inequality: $f \geq 6$
• For $f=7$: true