Solving Multi-Step Equations with Variables on Both Sides – Practice Problems

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Do you need help? Watch the Video Lesson for this Practice Problem. Solving Multi-Step Equations with Variables on Both Sides

To solve complicated variable equations such as those with variables on both sides of the equal sign, remember what you know about the balance scale – you must perform the same operation on both sides of the scale in order to stay balanced.

There are many steps to solve multi-step equations, hence the name. Step 1, if parentheses are shown in the equation, you may need to use the Distributive Property to simplify. Step 2, combine like terms on each side of the equal sign.

Like terms can be constants, variables alone, or variables with coefficients. Constants are numbers alone such as 3 or 1.5. Coefficients are numbers that are attached to a variable as a result of multiplication or division such as 2x or x/4.

Step 3, use the inverse operations (opposite operations) of addition or subtraction to move constants to one side of the equal sign and variables to the other. Use common sense, and do this in the most efficient manner. Next is Step 4, use inverse operations of multiplication or division to isolate the variable and calculate the answer. It’s always a good idea to check your work by substituting the solution for the variable back into the original equation and use PEMDAS to simplify.

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

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Exercises in this Practice Problem
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Decide which steps are needed to solve the equation $3\times (2x-5)+10=4x+9$.
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Evaluate how we can solve an equation.
Solve the following equations.