Solving Equations With Variables on Both Sides

An equation can have variable terms on both sides. When solving this type of equation, it is necessary to transfer all the variable terms to one side. Once all variable terms are on the same side, they can be combined. Consider an example equation with variable terms on both sides. 3x=x-2 There are three main steps to follow when solving this type of equation.

Transferring Variable Terms to One Side

Inverse operations and the Properties of Equality are used to move all the variable terms to one side of the equation. In this case, the Subtraction Property of Equality is used to subtract x from both sides of the equation. 3x &= x-2 &⇓ 3x - x &= x -2 - x

Combining Like Terms

Then, the equation is simplified by combining like terms. This results in an equation with just one variable term. 3x - x &= x -2 - x &⇓ 2x &= - 2

Solving the Resulting Equation

The resulting equation can then be solved like a regular equation.

2x = - 2

DivEqn

.LHS /2.=.RHS /2.

2x/2 = - 2/2

CalcQuot

Calculate quotient

x = - 1

The solution to the given equation is x = - 1.

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