Solve the following inequality algebraically. \[ 5|x+2|-1>24 \]

To solve the inequality \( 5|x+2|-1>24 \), we start by isolating the absolute value expression. 1. Add 1 to both sides: \[ 5|x+2| > 25 \] 2. Divide both sides by 5: \[ |x+2| > 5 \] Next, we need to split this absolute value inequality into two separate inequalities: 1. \( x + 2 > 5 \) 2. \( x + 2 < -5 \) Now, we solve each inequality: 1. For \( x + 2 > 5 \): \[ x > 3 \] 2. For \( x + 2 < -5 \): \[ x < -7 \] Thus, the solution to the inequality \( 5|x+2|-1>24 \) is: \[ x < -7 \quad \text{or} \quad x > 3 \] In interval notation, the solution can be expressed as: \[ (-\infty, -7) \cup (3, \infty) \]