The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation.
To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation. Performing the same operation on both sides of an equation does not change the validity of the equation, or the value of the variable that satisfies it.
When more than one operation acts on a variable in an algebraic equation, apply the reverse of the order of operations to reverse the operations. Here is the order in which you should reverse operations:
Example 1: Solve for
5x + 9 = 44
Example 2: Solve for
3( - 1) = 15
Example 3: Solve for
4(3(z - 11) + 6) = 48
Sometimes, the equation will not start out simplified. If this is the case, simplify the equation before reversing the operations.
Example 4: Solve for
6x - 5 - 2x + 3 - 2 = 4
First, simplify the equation by combining like terms: 4x - 4 = 4