1. The problem is to match each inequality with the correct graph description. 2. Let's analyze each inequality and graph: - For $x \geq 12$: The inequality means $x$ is greater than or equal to 12, so the graph should have a closed circle at 12 and an arrow pointing right (greater values). - For $w < -2$: The inequality means $w$ is less than -2, so the graph should have an open circle at -2 and an arrow pointing left (less values). - For $y \leq 0$: The inequality means $y$ is less than or equal to 0, so the graph should have a closed circle at 0 and an arrow pointing left. - For $p > -20$: The inequality means $p$ is greater than -20, so the graph should have an open circle at -20 and an arrow pointing right. 3. Now, match these with the given graph descriptions: - "A red line with an open circle on the right side and an arrow pointing left" corresponds to $w < -2$. - "A red line with an open circle on the left side and an arrow pointing right" corresponds to $x \geq 12$ (but since $x \geq 12$ requires a closed circle, this description is incorrect for $x \geq 12$; the correct match is the one with a closed circle on the left and arrow right for $p > -20$). - "A red line with a closed circle on the right side and an arrow pointing left" corresponds to $y \leq 0$. - "A red line with a closed circle on the left side and an arrow pointing right" corresponds to $p > -20$ (but $p > -20$ requires an open circle, so this description is incorrect for $p > -20$). 4. Correct matches based on the inequalities and graph descriptions: - $w < -2$: open circle right side, arrow left. - $x \geq 12$: closed circle left side, arrow right (not open circle). - $y \leq 0$: closed circle right side, arrow left. - $p > -20$: open circle left side, arrow right. 5. Final matching: - $w < -2$ matches "A red line with an open circle on the right side and an arrow pointing left." - $x \geq 12$ matches "A red line with a closed circle on the left side and an arrow pointing right." - $y \leq 0$ matches "A red line with a closed circle on the right side and an arrow pointing left." - $p > -20$ matches "A red line with an open circle on the left side and an arrow pointing right."