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When solving equations, sometimes more than one step is needed. Both the number of steps and the operations required depend on the complexity of the given equation. For example, consider the following pair of equations.
rl Equation (I):& 3/2(x-2)+5 = 14 [0.8em] Equation (II):& y+2y-4 = 11-2y
The general idea is to simplify both sides of the equation and then isolate the variable on one side of the equation. This is usually done by collecting all the variable terms on one side of the equations and combining them. Then, the operations applied to the variable are undone in reverse order.
Equation (I) contains a fraction and parentheses. 3/2(x-2)+5=14
Distribute 3/2
a/2* 2 = a
Add terms
The coefficient of the variable is a fraction. The Multiplication Property of Equality can be used to multiply both sides of the equation by the reciprocal of the coefficient.
LHS * 2/3=RHS* 2/3
Commutative Property of Multiplication
a/b* b/a=1
1* a=a
a*b/c= a* b/c
Multiply
Calculate quotient
As such, x=8 is the solution of Equation (I).
In this equation, the variable is on both sides of the equation. y+2y-4=11-2y Solving the equation will require the additional step of collecting the variables on one side of the equation.
LHS+2y=RHS+2y
Commutative Property of Addition
Add terms
LHS+4=RHS+4
Add terms
.LHS /5.=.RHS /5.
Calculate quotient
In conclusion, y=3 is the solution of Equation (II).
Note that the operations used to solve Equations (I) and (II) may not be the same as those required to solve a different equation.