Express the set \( -4 x+30 \leq 2 x+12 \) using interval notation.

To solve the inequality \( -4x + 30 \leq 2x + 12 \) and express the solution in interval notation, follow these steps: 1. **Combine like terms:** \[ -4x + 30 \leq 2x + 12 \] Subtract \( 2x \) from both sides: \[ -6x + 30 \leq 12 \] Subtract \( 30 \) from both sides: \[ -6x \leq -18 \] 2. **Solve for \( x \):** Divide both sides by \( -6 \). Remember to reverse the inequality sign when dividing by a negative number: \[ x \geq 3 \] 3. **Express in interval notation:** \[ [3, \infty) \] **Final Answer:** \(\boxed{\,\left[\,3,\;\infty\,\right)}\)