Solving Multi-Step Equations with Variables on Both Sides

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Susan S.

Basics on the topicSolving 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

TranscriptSolving Multi-Step Equations with Variables on Both Sides

Meet Emilio and Joanna. They're at a fish store. They've come to buy some scaly friends, and they each have the same amount of money.

Emilio makes his selection quickly. He buys two Rainbow Blinkeys and ten Grey Borings. Joanna loves Rainbow Blinkeys, so she buys five of them and just one Grey Boring. They both spend all of their money.

When Emilio sees Joanna’s purchase, he feels sad because he realizes he could have bought another Rainbow Blinkey. He wonders, to get one more Rainbow Blinkey, how many Grey Borings would he need to exchange? To find out how many, Emilio can use a multi-step equation with variables on both sides of the equal sign.

Multi-step Equation Example 1

Just to refresh your memory, an equation works like a scale. And to keep the scale balanced, when you add or subtract one side of the scale, you must perform the same operation to the other side.

Joanna bought five Rainbow Blinkeys and one Grey Boring. For the same amount of money, Emilio bought two Rainbow Blinkeys and ten Grey Borings so the scale is balanced.