Solving Multi-Step Equations with Variables on One Side – Practice Problems

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Linear equations needing more than one step to solve are called multi-step equations. When the variable is on just one side of the equal sign, you can follow these steps to solve for the value of the unknown variable.

First, if there are parentheses, use the Distributive Property to multiply the number outside the parentheses across the terms that are inside the parentheses. Second combine all the like terms. Numbers alone, also called constants, are like terms, and same variables and same variables attached to numbers, known as a coefficients, are also like terms. The third step, you can use opposite (inverse) operations in the order of reverse PEMDAS. To isolate the variable, use inverse (opposite) operations to add or subtract on both sides of the equal sign, then use inverse operations to multiply or divide to completely isolate the variable leaving, finally, the solution to the linear equation.

After following the multiple steps of multi-step equations, there is one final step – check your work. You can do this by substituting the value of the variable back into the original equation, and use the order of operations (PEMDAS, BEDMAS, BODMAS, BIDMAS, operator precedence) to simplify. If you have solved the equation correctly, the left side of the equal sign will be the same as the right side.

Explain steps to solve algebraic equations. CCSS.MATH.CONTENT.HSA.REI.A.1

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