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:

\( x \leq -8 \)