Absolute Value Equation Game (Level 3)

Absolute Value Equation Game (Level 3)
This game is a level-up from Level 1 and Level 2. You aren’t just looking for a number and its negative; you now have to solve two equations for every problem (Split and Solve method).
Scroll down the page for a more detailed explanation.
 
Check out these other Absolute Value Equation games:
Solve Absolute Value Equations: Level 1 (|x|=a)
Solve Absolute Value Equations: Level 2 (|x| ± a=b, a|x|=b)
Solve Absolute Value Equations: Level 3 (|x ± b|=a)
Solve Absolute Value Equations: Level 4 (k|x ± b|=a)
 

 

How to play the “Absolute Value Equation Game”
Solve absolute value equations of the form |x ± b| = a

1. Analyze the Right Side (a)
   Before you start calculating, look at what the absolute value is equal to.
   If it’s negative (e.g., = -5): Click “No Solution” immediately. Distance cannot be negative.
   If it’s positive (e.g., = 10): You need to find two different values for x.
   
   
2. The “Split and Solve” Method
   To find the two numbers, you must mentally (or on scratch paper) create two paths:
   Path 1 (The Positive): Remove the bars and solve as is.
   Example: |x + 2| = 5 → x + 2 = 5 → x = 3
   Path 2 (The Negative): Remove the bars and make the right side negative.
   Example: |x + 2| = 5 → x + 2 = -5 → x = -7
   
   
3. Select and Submit
   Click both solutions (e.g., 3 and -7). They will turn blue.
   Click “Check Solutions”.
   If you are correct, they turn green. If you missed one or picked a wrong number, the game will show you the correct answers in red/green.
    
   

How to solve absolute equations of the form |x±b|=a

1. Check for “No Solution”
   Before doing any math, look at the value of a (the number on the right side).
   If a < 0: There is No Solution. Absolute value represents distance, and distance can never be negative.
   If a = 0: There is exactly one solution.
   If a > 0: There are two solutions.
   
   
2. Split the Equation
   If a is positive, you must remove the absolute value bars by “splitting” the equation into two separate linear equations. This accounts for both the positive and negative directions on the number line.
   Create these two cases:
   Case 1 (Positive): x + b = a
   Case 2 (Negative): x + b = -a
   
   
3. Solve for x
   Solve both equations by isolating x.
   This usually involves using inverse operations to move b to the other side.
   
   Example:
   |x + 5| = 12
   Equation 1: x + 5 = 12
   Subtract 5 from both sides: x = 7
   Equation 2: x + 5 = -12
   Subtract 5 from both sides:
   x = -17
   Final Solution: x = {7, -17}
   
    
   

This video gives a clear, step-by-step approach to solving absolute value equations.

• Show Video

 

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