Solve the inequality and determine the graph of the solution set. Express the solution set using interval notation. \( -7<2 x+1 \leq 3 \)

To solve the compound inequality \( -7 < 2x + 1 \leq 3 \), we'll break it into two parts. First, solve \( -7 < 2x + 1 \): 1. Subtract \( 1 \) from both sides: \( -7 - 1 < 2x \) \( -8 < 2x \) 2. Divide by \( 2 \): \( -4 < x \) or \( x > -4 \). Now, solve \( 2x + 1 \leq 3 \): 1. Subtract \( 1 \) from both sides: \( 2x \leq 3 - 1 \) \( 2x \leq 2 \) 2. Divide by \( 2 \): \( x \leq 1 \). Combining both parts, we have \( -4 < x \leq 1 \). In interval notation, the solution set is \((-4, 1]\). For the graph of this solution, you would represent it on a number line with an open circle at \(-4\) (indicating it's not included) and a filled circle at \(1\) (indicating that \(1\) is included), shading the portion of the line between those two points.