Express the following inequality a) using a number line, b) in interval notation, and c) as a solution set (use set builder notation). a> -2 and \( \mathrm{a} \leq 4 \)

To visualize the inequality on a number line, you would draw a line and place a solid dot at -2 (indicating that -2 is not included) and a solid dot at 4 (indicating that 4 is included). You then shade the region between these two points, showing that all values of \( a \) greater than -2 and up to and including 4 are part of the solution. In interval notation, the solution can be expressed as \( (-2, 4] \). This denotes all the numbers greater than -2 but less than or equal to 4, clearly outlining the range of values that satisfy the inequality. As a solution set in set builder notation, we can express it like this: \( \{ a \in \mathbb{R} \mid -2 < a \leq 4 \} \). This reads as "the set of all real numbers \( a \) such that \( a \) is greater than -2 and less than or equal to 4."