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Solving an Algebraic Equation

Part of the Basic Math & Pre-Algebra Workbook For Dummies Cheat Sheet

An algebraic equation is an equation with at least one variable. Apply operations equally to both sides to modify an equation. For example, you can add 2 to both sides, subtract x from both sides or multiply both sides by 2. To solve an algebraic equation, apply operations that isolate x on one side of the equation and put a number on the other side. Here are the standard steps for a problem such as 10x – 6 = 7x + 9:

  1. Add or subtract to move all the constants to one side of the equation.

    If you add 6 to both sides, the –6 cancels out on the left: 10x = 7x + 15.

  2. Add or subtract to move all the variables to the other side.

    If you subtract 7x from both sides, the 7x cancels out on the right: 3x = 15.

  3. Divide both sides by the coefficient (the number next to the variable) to isolate x.

    Dividing both sides by 3 gives you the answer x = 5.

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