Solve the inequality involving absolute value. Write your final answer in interval notation. (If the solution set is empty, enter EMPTY or \( \varnothing \).) \[ |2 x+1|+1 \leq 8 \] +

To solve the inequality \( |2x + 1| + 1 \leq 8 \), we first isolate the absolute value: \[ |2x + 1| \leq 8 - 1 \] \[ |2x + 1| \leq 7 \] This means we can split it into two separate inequalities: 1. \( 2x + 1 \leq 7 \) 2. \( 2x + 1 \geq -7 \) Now, let's solve each inequality: 1. For \( 2x + 1 \leq 7 \): \[ 2x \leq 6 \quad \Rightarrow \quad x \leq 3 \] 2. For \( 2x + 1 \geq -7 \): \[ 2x \geq -8 \quad \Rightarrow \quad x \geq -4 \] Combining these results, we find: \(-4 \leq x \leq 3\) In interval notation, the solution is: \([-4, 3]\)