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:

\(x < 15\)