Select the correct answer. Which graph represents the solution to the inequality? -2.4(x − 6) ≥ 52.8 A. A number line ranges from negative 22 through negative 2 from left to the right in increments of 2. A solid circular point is at negative 16

To solve the inequality \(-2.4(x - 6) \geq 52.8\), we start by isolating \(x\). 1. Distribute \(-2.4\): \[ -2.4x + 14.4 \geq 52.8 \] 2. Subtract \(14.4\) from both sides: \[ -2.4x \geq 52.8 - 14.4 \] \[ -2.4x \geq 38.4 \] 3. Divide both sides by \(-2.4\). Remember to flip the inequality sign when dividing by a negative number: \[ x \leq \frac{38.4}{-2.4} \] \[ x \leq -16 \] Now, the solution set is \(x \leq -16\). This means we have a solid circle at \(-16\) and an arrow extending to the left on a number line. Looking at the options provided: - **Option A:** A solid circular point at -16 with an arrow extending to the left (which matches our solution). - **Option B:** A solid circular point at -16 with an arrow extending to the right (incorrect). - **Option C:** A solid circular point at -8 with an arrow extending to the left (incorrect). - **Option D:** A solid circular point at -8 with an arrow extending to the right (incorrect). The correct answer is **A**.