Inequalities on a Number Line

x > 5 is true for 6, for 5.1, and for a million. An inequality has no single answer.

Drawing it

Mark 5, then shade every number to the right of it.

Open or closed

x > 5 leaves 5 out, so the circle is open. x ≥ 5 includes it, so the circle is filled.

Reading the symbol

The wide end faces the larger side. In x > 5 the wide end faces x, so x is the bigger one.

Drawing the solution

For n > 5, draw an open circle at 5 and shade everything to the right. The open circle means 5 itself is not included. For n ≥ 5, fill the circle in. The drawing encodes both the range and whether the endpoint counts.

Which way to shade

Shade the side containing the numbers that make the inequality true. Test one: is 6 > 5? Yes, so shade towards 6. Testing a single point is more reliable than trying to remember which symbol points which way.

Solving works the same way

For n + 3 > 8, subtract 3 from both sides to get n > 5. Inequalities are solved by the same balance reasoning as equations. One caution for later: multiplying or dividing both sides by a negative flips the direction of the symbol.

Context can cut the range down

If n is a number of people, n > 5 really means 6, 7, 8 and so on — not 5.5. The mathematics allows every real number above 5, but the situation may only allow whole ones. Saying so is part of a complete answer.