Graphing Inequalities with x>4- A Step-by-Step Guide

What Does x>4 Actually Mean?

When you see x > 4, it's asking a simple question: which numbers are bigger than 4? The answer is every number to the right of 4 on the number line. That's it. No tricks.

The > symbol means "greater than." It does not include the number itself. So 4 is not a valid answer. But 4.0001, 5, 100, and infinity all work.

This guide shows you exactly how to graph it, step by step.

The Number Line Foundation

Before you graph anything, you need to know how a number line works.

• Numbers increase going right
• Numbers decrease going left
• Zero sits in the middle
• Positive numbers go right, negative numbers go left

Once you have this down, plotting x > 4 takes about 10 seconds.

Graphing x > 4 on a Number Line

Step 1: Draw the Number Line

Sketch a horizontal line. Add tick marks at regular intervals. Label at least 0, 4, and maybe -2 or 5 for context.

Step 2: Locate the Number 4

Find 4 on your number line and mark it clearly. This is your boundary point.

Step 3: Draw an Open Circle at 4

Place an open circle (hollow circle, not filled in) directly on top of 4. This tells readers that 4 itself is not included in the solution.

This is where most students mess up. They use a closed circle and suddenly 4 becomes part of the answer. That's wrong.

Step 4: Shade Everything to the Right

Draw a solid line or arrow starting from the open circle and extending to the right edge of your number line. Include all values greater than 4.

Step 5: Add an Arrowhead

Finish the line with an arrow pointing right. This signals "and keeps going forever." Because it does.

Open Circle vs Closed Circle: The Critical Difference

This trips up almost everyone at first.

• Open circle: the number is NOT included. Use with > (greater than) or < (less than)
• Closed circle: the number IS included. Use with ≥ (greater than or equal) or ≤ (less than or equal)

For x > 4, you use an open circle because 4 doesn't count. If the problem was x ≥ 4, you'd use a closed circle.

Memorize this now. It comes back on every test.

Graphing x > 4 in Two Dimensions (Cartesian Plane)

If you're working on an x-y graph instead of a number line, the approach changes slightly.

For x > 4, you draw a dashed vertical line at x = 4. Then shade the entire region to the right of that line.

The dashed line means points on x = 4 are not included. The shading shows all points where x is greater than 4.

Common Mistakes to Avoid

• Using a closed circle when you need an open one — check your inequality symbol every time
• Shading the wrong direction — > means right/up, < means left/down
• Forgetting the arrow — your graph should show the solution extends infinitely
• Mixing up number lines and coordinate planes — they're different tools for different problems

Quick Reference Table

How to Check Your Work

Pick any number in your shaded region. Plug it into the original inequality. If it works, your graph is probably correct.

For x > 4:

• Test x = 5 → 5 > 4 ✓
• Test x = 100 → 100 > 4 ✓
• Test x = 4 → 4 > 4 ✗ (correct, 4 shouldn't work)

If 4 passes your test, you used the wrong circle. Go back and fix it.

That's the Whole Process

Graphing x > 4 comes down to three things: open circle at 4, shade right, add an arrow. Everything else is just context.

Once you internalize the difference between open and closed circles, you'll graph any inequality correctly on the first try.