Solving Equations by Using Inverse Operations
Inverse operations "undo" or reverse each other's results. Addition and subtraction are inverse operations which cancel each other out.
Multiplication and division are also inverse operations that will cancel each other out.
We can use inverse operations to solve many types of equations. To do this, we determine the operations that were applied to the variable to build the equation. We then use inverse operations to isolate the variable by "undoing" these operations.
Ex. 1: Find the value of x in the following equation by using inverse operations.
2x + 3 = 11
Steps
1) Start with the variable and build
Build Equation
the equation following the rules of BEDMAS. This means the multiplying
is done before the adding.
2) Solve the equation for the variable
by using inverse operations. You will
be doing reverse BEDMAS.
Solve Equation
According to the diagram, the answer to 2x + 3 = 11 is x = 4.
Ex. 2: Solve the equation below for x by using inverse operations and an algebraic solution.
3x ­ 5 = 7
Method 1 (Inverse Operations)
Method 2 (Algebraic Solution)
Build Equation using BEDMAS
To solve algebraically, just use reverse BEDMAS and isolate the variable. Remember whatever you do
to one side of an equation, you must do to the opposite
side.
Solve Equation using Reverse
BEDMAS
1
2