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.
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.