Absolute Value Equation Game (Level 2)

To solve an absolute value equation of the form |x|+b=a, |x|-b=a or b|x|=a, you are essentially finding all values of x that are exactly a units away from the point -b on a number line. Since absolute value measures distance from a point, most equations will have two solutions.

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Absolute Value Equation Game (Level 2)
This game is a level-up from Level 1. In this level, the absolute value bars |x| are not alone. You need is to isolate the bars by moving the outside numbers to the other side of the equation before you try to find the values for x.
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 Solve the Two Equation Types
Type 1: The Addition/Subtraction Model (|x| ± a = b)
You need to move the constant a to the other side using the opposite sign.
If you see |x| + 5 = 12: Subtract 5 from 12. You get |x| = 7.
If you see |x| - 3 = 10: Add 3 to 10. You get |x| = 13.

Type 2: The Multiplication Model (a|x| = b)
The number a is stuck to the bars. You must divide both sides by a.
If you see 3|x| = 15: Divide 15 by 3. You get |x| = 5.
If you see 2|x| = 0: Divide 0 by 2. You get |x| = 0

Reading the “Isolated” Result
Once you have the bars alone (|x| = number), look at that number to decide your answer:
Positive (e.g., 5): Select the positive and negative number (5 and -5).
Zero (0): Select only 0.
Negative (e.g., -4): Select No Solution.

Gameplay Steps

Calculate: Mentally isolate the bars.
Select: Click the buttons in the grid that match your final x values.
Tip: If the isolated result is positive, you must pick two buttons.
Check: Hit “Check Solutions”.
Green: Correct.
Red: Incorrect
Repeat: Click “Next Equation”.

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

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