Question

solve the inequality.
$8 - \frac{1}{4}n \geq 20$
$n \square \square$
(type an integer or a decimal.)

Explanation:

Step1: Subtract 8 from both sides

To isolate the term with \( n \), we subtract 8 from both sides of the inequality \( 8 - \frac{1}{4}n \geq 20 \). This gives us \( 8 - 8 - \frac{1}{4}n \geq 20 - 8 \), which simplifies to \( -\frac{1}{4}n \geq 12 \).

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

When we multiply or divide an inequality by a negative number, we must reverse the inequality sign. So, multiplying both sides of \( -\frac{1}{4}n \geq 12 \) by -4 gives \( (-4) \times (-\frac{1}{4}n) \leq (-4) \times 12 \). Simplifying both sides, we get \( n \leq -48 \).

Answer:

\( n \leq -48 \)