1. **State the problem:** Represent the inequality $-2 < x \leq 4$ on the number line. 2. **Understand the inequality:** The inequality $-2 < x \leq 4$ means $x$ is greater than $-2$ but less than or equal to $4$. 3. **Number line representation rules:** - Use an open circle at $-2$ because $x$ is strictly greater than $-2$ (not including $-2$). - Use a closed circle at $4$ because $x$ can be equal to $4$. - Shade the region between $-2$ and $4$ to show all values $x$ can take. 4. **Draw the number line:** - Mark points from $-5$ to $6$. - Place an open circle at $-2$. - Place a closed circle at $4$. - Shade the line segment between $-2$ and $4$. --- 1. **State the problem:** Find the value of $x$ in the diagram where three identical rhombuses meet, with angles $70^\circ$, $70^\circ$, $70^\circ$, and $x^\circ$ around a point. 2. **Formula and rule:** The sum of angles around a point is $360^\circ$. 3. **Set up the equation:** $$70 + 70 + 70 + x = 360$$ 4. **Simplify:** $$210 + x = 360$$ 5. **Solve for $x$:** $$x = 360 - 210$$ $$x = 150$$ 6. **Interpretation:** The unknown angle $x$ is $150^\circ$. --- **Final answers:** - The inequality $-2 < x \leq 4$ is represented on the number line with an open circle at $-2$, a closed circle at $4$, and shading between them. - The value of $x$ in the rhombus diagram is $150^\circ$.