Question

solve the following inequality: 3 > \frac{x - 3}{4}

Explanation:

Step1: Multiply both sides by 4

To eliminate the denominator, we multiply both sides of the inequality \(3 > \frac{x - 3}{4}\) by 4. Since 4 is positive, the direction of the inequality sign remains the same.

$$ 3\times4 > \frac{x - 3}{4}\times4 $$

$$ 12 > x - 3 $$

Step2: Add 3 to both sides

To solve for \(x\), we add 3 to both sides of the inequality \(12 > x - 3\).

$$ 12 + 3 > x - 3 + 3 $$

$$ 15 > x $$

Which can also be written as \(x < 15\).

Answer:

\(x < 15\)