How Do You Solve Equations With PEMDAS?


Quick Answer

PEMDAS, or Please Excuse My Dear Aunt Sally, is the mnemonic device for order of mathematical operations used to solve algebraic equations. It represents parentheses, exponents, multiplication, division, addition and subtraction. Equations cannot just be solved left-to-right because the proper order of operations must be observed.

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How Do You Solve Equations With PEMDAS?
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Full Answer

  1. Solve parts of an equation that occur within parentheses

    Use the example equation (4x + 3x) - 5 + 4 - 10x/5 = 4 as a starting point. The terms 4x and 3x are in parentheses so these should be added first.

  2. Resolve exponents if any exist

    To avoid confusion, the terms inside parentheses are solved first and the exponent is applied to the variable. The coefficient is not affected.

  3. Multiply and divide terms that call for it

    Dividing 10x by 5 yields 2x. The equation is simplified to 7x - 5 + 4 - 2x = 4.

  4. Add and subtract as necessary by combining like terms

    Like terms are variables of the same degree or power to which they are raised. 7x - 2x leaves 5x, and adding -5 and 4 leaves -1.

  5. Isolate the variable

    After all like terms have been simplified, the equation is 5x - 1 = 4. Adding 1 to both sides yields 5x = 5, and x is 1. After solving, check the original equation.

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