How Do You Solve Algebraic Equations?


Quick Answer

The way to solve an algebraic equation depends on the equation. The order of operations (parenthesis, exponents, multiplication, division, addition, subtraction) can be used backwards as a guide for the solution.

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Full Answer

  1. Determine what is to be solved for

    Algebraic equations may have one or more variables, and so it is important to know what is being asked to solve for. For example, an equation may have one variable (3x + 3 = 18) or two variables (y - 3x =18). To begin solving any equation, it is important to know what to solve for. The question may state to solve for any of the variables contained in the equation.

  2. Solve the equation by doing the same thing on both sides

    The solution to an equation may be discovered by using the order of operations backwards. To begin finding the value of x in the example 3x + 3 = 18, simply subtract 3 from both sides of the equation. This cancels out the 3 on the left side and brings the number on the right side to 15, so the equation is now 3x = 15. Finally, divide both sides by 3, which reveals that the value of x is 5. Note that the same procedure is always done to both sides of the equation.

  3. Check the answer

    The answer is checked to make sure that it is correct by plugging the found value of x back into original equation. In the example above, this would be 3 * 5 + 3 =18. Solving the left-hand side using the order of operations forwards, yields that 18 = 18, which is true.

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