Solve for \( x \) : \[ -4(x+8)+2 \geq 2 x+3 \]

To solve the inequality \(-4(x+8)+2 \geq 2x+3\), we start by distributing \(-4\) on the left side: \[ -4x - 32 + 2 \geq 2x + 3 \] This simplifies to: \[ -4x - 30 \geq 2x + 3 \] Next, we move all terms involving \(x\) to one side and constant terms to the other side. First, we can add \(4x\) to both sides: \[ -30 \geq 6x + 3 \] Then, we subtract \(3\) from both sides: \[ -33 \geq 6x \] Next, we divide both sides by \(6\) (remembering to flip the inequality sign if we were dividing by a negative number, but since we're not in this case, it remains the same): \[ -\frac{33}{6} \geq x \] This can be simplified to: \[ -\frac{11}{2} \geq x \] Thus, we can rewrite it as: \[ x \leq -\frac{11}{2} \] So the solution to the inequality is: \[ x \leq -5.5 \]