How to Solve Algebraic Equations With a Variable
Variables are letter representations for unknown quantities. Equations contain expressions (numbers and variables combined with algebraic operations) set equal to each other or a constant (number). The purpose of a single variable equation is to solve for that variable to eliminate the unknown quantity from the statement. Equations can be simple or complex but all follow similar methods of solving. It's important to remember the order of operations in working algebra. The order is represented by the acronym PEMDAS: parenthesis, exponents, multiplication, division, addition and subtraction.
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Instructions
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Use algebra to solve a single variable algebraic equation. Work to isolate the variable on one side of the equal sign. Use opposites to cancel out terms (applying the changes to both sides) and stick to the order of operations.
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Solve the example algebraic equation 4x + 10 = x - 1/3. Subtract 10 from both sides: 4x = x - 1/3 - 10. Subtract "x" from both sides: 3x = 1/3 - 10. Convert 10 to the fraction 30/3 to perform the fractional subtraction: 3x = 1/3 - 30/3 or 3x = 29. Divide both sides by 3: x = 29 / 3.
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Leave the answer in improper fraction form or use a calculator to divide 29 by 3 for a result of 9.666... with the "6" in the decimal repeating forever. Round the answer to x = 9.67.
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