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# What are some examples of multistep equations with variables on both sides?

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### Quick Answer

Multistep equations with variables on both sides include 4x + 3 = 8x + 6, 2y + 7 = 4y - 2, 2x + 3y = 4(x - 1) + 2y and 3z(x + 4) = 2z + 3xy. Each equation is solved by moving terms from one side of the equal sign to the other side until the desired variable is isolated.

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### Full Answer

Equations are balanced using the addition and multiplication properties of equality. The addition property of equality states that an equation remains balanced when a term is added to both sides of an equation. The multiplication property of equality states that an equation remains balanced when both sides of an equation are multiplied by a nonzero number.

For example, in the equation x - 4 = 6, the addition property is used to add four to each side and isolate x. The result is x = 10. When solving the equation x/4 = 2, the multiplication property is used to multiply both sides by four. The result is x = 8.

Since many equations have multiple different variables, the solution to these equations can change by solving for different variables. In the equation x + 3 = y - 5, the solution is either x = y - 8 or y = x + 8. Because of this, multiple variable algebra problems state to solve for a specific variable.

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