1. The problem involves understanding and comparing the inequalities: $x < 80$, $x \geq 80$, and $x > 80$. 2. Inequalities describe ranges of values for $x$: - $x < 80$ means all values less than 80. - $x \geq 80$ means all values greater than or equal to 80. - $x > 80$ means all values strictly greater than 80. 3. These inequalities split the number line at 80 into different regions: - $x < 80$ covers values to the left of 80. - $x \geq 80$ covers 80 and all values to the right. - $x > 80$ covers values strictly to the right of 80, excluding 80 itself. 4. The difference between $x \geq 80$ and $x > 80$ is the inclusion of the point 80. 5. Graphically, these can be represented as three circles aligned vertically, each containing one inequality: - Top circle: $x < 80$ - Middle circle: $x \geq 80$ - Bottom circle: $x > 80$ 6. This visualization helps understand how the inequalities partition the number line and their relationships. Final answer: The inequalities represent distinct ranges with $x < 80$ and $x \geq 80$ covering all real numbers without overlap except at 80, and $x > 80$ excluding 80 itself.