Question

How does the solution to an inequality differ from the solution to an equation?

Answer 1

The solution to an inequality generally is a region with one more dimension.

If the inequality/equation is of the form x < a or x = a then the solution to the inequality is the 1 dimensional line segment while the solution to the equality is a point which has no dimensions.

If the inequality/equation is in 2 dimensions, the solution to the inequality is an area whereas the solution to the equality is a 1-d line or curve.

And so on, in higher dimensional spaces.