Solve the inequality. \( \begin{array}{l}\frac{x}{4} \leq x+3 \\ x \geq[?]\end{array} \)

To solve the inequality \(\frac{x}{4} \leq x + 3\), start by eliminating the fraction. Multiply both sides by 4 (remembering that this won't change the inequality since 4 is positive), giving us: \[ x \leq 4(x + 3) \] Expanding the right-hand side results in: \[ x \leq 4x + 12 \] Next, we isolate \(x\) by moving terms involving \(x\) to one side: \[ x - 4x \leq 12 \] This simplifies to: \[ -3x \leq 12 \] Now, divide both sides by -3. Remember that dividing by a negative number flips the inequality sign: \[ x \geq -4 \] So, the solution to the inequality is: \[ x \geq -4 \]