Question

2 - \frac{x}{4} \geq 4

Explanation:

Step1: Subtract 2 from both sides

To isolate the term with \( x \), we subtract 2 from both sides of the inequality \( 2 - \frac{x}{4} \geq 4 \).
\[
2 - \frac{x}{4} - 2 \geq 4 - 2
\]
Simplifying both sides, we get:
\[
-\frac{x}{4} \geq 2
\]

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

When multiplying or dividing an inequality by a negative number, we reverse the inequality sign. We multiply both sides by -4.
\[
-\frac{x}{4} \times (-4) \leq 2 \times (-4)
\]
Simplifying both sides, we get:
\[
x \leq -8
\]

Answer:

\( x \leq -8 \)