1. **State the problem:** We need to determine which inequality corresponds to the solution set shown on the graph. The graph shows an open circle at $-2$ and shading to the right, indicating the solution set is all values $m > -2$. 2. **Analyze each inequality:** - Option A: $-4.5 > -3.2m + 1.9$ - Option B: $-4.5 < -3.2m + 1.9$ - Option C: $-4.5 > 3.2m + 1.9$ - Option D: $-4.5 < 3.2m + 1.9$ 3. **Solve each inequality for $m$ to find the solution set:** **Option A:** $$-4.5 > -3.2m + 1.9$$ Subtract 1.9 from both sides: $$-4.5 - 1.9 > -3.2m$$ $$-6.4 > -3.2m$$ Divide both sides by $-3.2$ (note: dividing by a negative reverses inequality): $$\cancel{-3.2}m < \frac{\cancel{-6.4}}{-3.2}$$ $$m < 2$$ **Option B:** $$-4.5 < -3.2m + 1.9$$ Subtract 1.9: $$-6.4 < -3.2m$$ Divide by $-3.2$ (reverse inequality): $$m > 2$$ **Option C:** $$-4.5 > 3.2m + 1.9$$ Subtract 1.9: $$-6.4 > 3.2m$$ Divide by $3.2$ (positive, inequality stays): $$m < -2$$ **Option D:** $$-4.5 < 3.2m + 1.9$$ Subtract 1.9: $$-6.4 < 3.2m$$ Divide by $3.2$: $$m > -2$$ 4. **Compare with graph:** The graph shows $m > -2$, which matches Option D. **Final answer:** Option D: $-4.5 < 3.2m + 1.9$