Which of the following inequalities is equivalent to (|𝑥|+1)2≤4?

The given inequality is (|𝑥|+1)² ≤ 4.

Step 1: Take the square root on both sides of the inequality.

This gives us -2 ≤ |𝑥|+1 ≤ 2.

Step 2: Subtract 1 from all parts of the inequality.

This gives us -3 ≤ |𝑥| ≤ 1.

Step 3: Solve the absolute value inequality.

This gives us -1 ≤ 𝑥 ≤ 1.

So, the inequality equivalent to (|𝑥|+1)² ≤ 4 is -1 ≤ 𝑥 ≤ 1.