Solve the inequality |7x + 1| <= 0.

The inequality |7x + 1| <= 0 has only one solution, x = -1/7.

To solve the inequality |7x + 1| <= 0, we first note that the absolute value of any real number is always non-negative. Therefore, the left-hand side of the inequality is always non-negative, and the only way for the inequality to hold is if it is equal to zero. That is,

|7x + 1| = 0.

The only real number whose absolute value is zero is zero itself. Therefore, we must have

7x + 1 = 0.

Solving for x, we get

x = -1/7.

This is the only solution to the inequality, and it satisfies the original inequality since

|7(-1/7) + 1| = |-1 + 1| = 0 <= 0.

Therefore, the solution to the inequality |7x + 1| <= 0 is x = -1/7.