Question

solve the inequality.
\frac{x}{4} \leq x + 3

x \geq ?

Explanation:

Step1: Subtract \(x\) from both sides

\(\frac{x}{4}-x\leq x + 3-x\)
Simplify the left side: \(\frac{x}{4}-\frac{4x}{4}=\frac{x - 4x}{4}=-\frac{3x}{4}\), and the right side is \(3\). So we get \(-\frac{3x}{4}\leq3\).

Step2: Multiply both sides by \(-\frac{4}{3}\) (reverse inequality)

\(-\frac{3x}{4}\times(-\frac{4}{3})\geq3\times(-\frac{4}{3})\)
Simplify both sides: The left side is \(x\), and the right side is \(- 4\). So \(x\geq - 4\).

Answer:

\(-4\)