Write the inequality in interval notation and graph the interval. \( -5

Ask by Rowe Marsh. in the United States

Mar 08,2025

1. The inequality is given as: \[ -5 < x \leq 3 \] 2. To write this in interval notation, note that: - The inequality does not include \(-5\), so we use a parenthesis at \(-5\). - The inequality includes \(3\), so we use a bracket at \(3\). Thus, the interval notation is: \[ (-5, 3] \] 3. To graph the interval on a number line: - Draw a horizontal line and mark the points \(-5\) and \(3\). - Place an open circle at \(-5\) to indicate that \(-5\) is not included. - Place a closed circle at \(3\) to indicate that \(3\) is included. - Shade the region between \(-5\) and \(3\). The graph looks like this: \[ \begin{array}{ccccccccccc} \cdots & -6 & \quad -5 & \quad -4 & \quad \cdots & \quad 2 & \quad 3 & \quad 4 & \quad \cdots \\ & & \circ & \underline{\hspace{1cm}} & & \underline{\hspace{1cm}} & \bullet & & \\ \end{array} \] Here, the open circle \(\circ\) at \(-5\) indicates that \(-5\) is not included, and the filled circle \(\bullet\) at \(3\) indicates that \(3\) is included, with the region between them shaded.