Interactive Applet - Solving Linear Equations

Difficulty controls the equation type. You can move variable terms using inputs like 7x, -x, or even fractions like 1/2x.

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Tips
Move constants with numbers; move variable terms with kx (e.g., -3x). Clear fractions/decimals first. In Fractions mode, you can type inputs like 3/4 or -1/2x.

Progress

    Study Guide: How to Solve Linear Equations

    Core Goal

    Isolate x while keeping the equation balanced (do the same operation to both sides).

    Legal Moves (Properties of Equality)

    • Add/Subtract the same number or term (e.g., 7x) on both sides.
    • Multiply/Divide both sides by the same nonzero number.

    Strategy

    1. Simplify each side (distribute, combine like terms).
    2. Collect variable terms on one side and constants on the other.
    3. Scale to make the coefficient of x equal 1 (Multiply/Divide).
    4. Check by substitution.

    Special Cases

    • Identity (e.g., 6 = 6): infinitely many solutions (all real numbers).
    • Contradiction (e.g., 3 = 8): no solution.

    Fractions & Decimals

    • Fractions: Multiply both sides by the LCM to clear denominators.
    • Decimals: Multiply both sides by 10, 100, 1000, to shift place values.

    Quick Example (Fractions)

    Solve (1/2)x + 3/4 = 5, Multiply both sides by 4, 2x + 3 = 20 Subtract 3, 2x = 17 Divide by 2, x = 17/2.