Graph Inequality Number Line Game

Graphing Inequalities on a Number Line
Graphing an inequality creates a visual map of all the possible numbers that make a statement true. Unlike a standard equation (like $x = 5$), which is just a single dot, an inequality usually covers an entire section of the number line. Scroll down the page for a more detailed explanation.
 
This game will test your knowledge by presenting an inequality. You will need to indicate how the inequality will be represented on the number line. The inequalities are designed to help you identify the key differences between a strict inequality (> or <) and an inclusive one (≥ or ≤). If you give a wrong answer, the game will provide the correct answer.

 

 

How to Play the Master the Number Line Game
This game requires you to read the inequality and draw it on the number line by adjusting the position, direction, and circle type.
Here’s how to play:

1. Start Game: Click “Start Graphing”.
   
2. Look at the Problem: Graph the inequality shown. Draw it on the number line by adjusting the position, direction, and circle type .
   
3. Enter Your Answer: You need to select a symbol and enter a number to indicate the inequality shown.
   
4. Check Your Work: Click the “Check Graph”. The game will tell you if you’re correct or wrong,.
   
5. Get a New Problem: Click the “Next Problem” button for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
6. Back to Menu Click “Exit to Main Menu” to restart the game.
    
   

How to Graph Inequalities on a Number Line
The Four Symbols
To graph correctly, you must identify the symbol being used:
Symbol: >
Meaning: Greater than
Circle Type: Open (𓏸)
Arrow Direction: Right (→)

Symbol: <
Meaning: Less than
Circle Type: Open (𓏸)
Arrow Direction: Left (←)

Symbol: ≥
Meaning: Greater than or equal to
Circle Type: Closed (•)
Arrow Direction: Right (→)

Symbol: ≤
Meaning: Less than or equal to
Circle Type: Closed (•)
Arrow Direction: Left (←)

The Two Golden Rules Rule A: The Circle Rule
Open Circle (𓏸): Used for < and >. This means the starting number is not included in the solution.
Example: x > 5 means x could be 5.1 or 100, but it cannot be exactly 5.
Closed Circle (•): Used for ≤ and ≥. This means the starting number is included.
Example: x ≥ 5 means x can be exactly 5.

Rule B: The Direction Rule (The “Arrow Trick”)
If the variable (x) is on the left side of the inequality, the symbol actually points in the direction the arrow should go.
x > 5 (Points right →)
x < 5 (Points left ←)

Step-by-Step Example
Problem: Graph the inequality x ≤ -2
Find the “Boundary”: Locate -2 on the number line.
Choose the Circle: Because the symbol is “equal to” (≤), draw a closed circle at -2.
Pick the Direction: Since it is “less than,” the numbers are getting smaller. Shade the line and draw the arrow to the left.

Special Case: Flipping the Inequality
If you are solving an inequality and you multiply or divide by a negative number, you must flip the symbol before graphing.
Original: -2x < 10
Divide by -2: x > -5
Graph: An open circle at -5 with an arrow pointing to the right.
 

The video gives a clear, step-by-step approach on how to graph inequalities on the number line.

• Show Video

 

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