(4) \( |x+5|<12 \)

To solve the inequality \( |x+5|<12 \), we can split it into two separate inequalities. This means: 1. \( x + 5 < 12 \) 2. \( x + 5 > -12 \) From the first inequality, solving gives \( x < 7 \). From the second, solving gives \( x > -17 \). Therefore, the solution to the inequality \( |x+5|<12 \) is \( -17 < x < 7 \). To visualize this, consider the number line where you would plot the two points -17 and 7, and shade the region in between, demonstrating that all the values of \( x \) between -17 and 7 (but not including those endpoints) satisfy the original absolute value inequality!