Question

solve the inequality and graph the solution.
\\( 46 \leq \frac{f}{-4} + 45 \\)
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.
\\(\longleftarrow\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\vert\hspace{0.5cm}\longrightarrow\\)
\\( -5 \hspace{0.5cm} -4 \hspace{0.5cm} -3 \hspace{0.5cm} -2 \hspace{0.5cm} -1 \hspace{0.5cm} 0 \hspace{0.5cm} 1 \hspace{0.5cm} 2 \hspace{0.5cm} 3 \hspace{0.5cm} 4 \hspace{0.5cm} 5 \\)

Explanation:

Step1: Subtract 45 from both sides

To isolate the term with \( f \), we subtract 45 from both sides of the inequality \( 46 \leq \frac{f}{-4} + 45 \).

$$ 46 - 45 \leq \frac{f}{-4} + 45 - 45 $$

$$ 1 \leq \frac{f}{-4} $$

Step2: Multiply both sides by -4 (and reverse inequality)

When multiplying or dividing an inequality by a negative number, the direction of the inequality sign reverses. We multiply both sides by -4.

$$ 1 \times (-4) \geq \frac{f}{-4} \times (-4) $$

$$ -4 \geq f $$

Which can be rewritten as \( f \leq -4 \).

Answer:

The solution to the inequality is \( f \leq -4 \). To graph this, we plot a closed dot at -4 (since the inequality is "less than or equal to") and draw an arrow to the left (indicating all values less than -4 are included).