Inverse Operations and One Step Equations
Equation: is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are
written with an equal sign. Equations can also be used to state the equality of two expressions containing one or more
variables.
Numerical equation: this type of equation consists of numbers and there are no variables (example: 20 +30=50)
Algebraic equation: this type of equations contains at least one variable (example: 20 +x= 50)
When solving equations the goal is to isolate the variable on one side of the equation in order to determine its value
(the value that makes the equation true). In order to solve an equation containing a variable, you need to use
inverse (opposite/undoing) operations on both sides of the equation.
Inverses of each operation:
Addition: Subtraction
Multiplication: Division
Squaring: Square root
Cubing: Cube root
There are four properties of equality that we will use to solve equations:
Addition property: If a=b, the a +c= b +c for all real numbers a,b, and c. The same number can be added to each side
of the equation without changing the solution of the equation
Subtraction Property: If a=b, then a-c=b-c for all real numbers a,b, and c. The same number can be subtracted to each
side of the equation without changing the solution of the equation
Multiplication property: If a=b, then ac= bc for all real numbers a,b, and c. Each side of an equation can be multiplied
by the same number without changing the solution of the equation
Division Property: If a=b and c ≠ 0, then a ÷ c= b÷ c for all real numbers a,b, and c. Each side of an equation can be
divided by the same number without changing the solution of the equation
One step equations
The purpose of solving an equation is to find a solution. A solution is a value that can replace the variable in order to
make the equation true.
To solve equations, you must work backwards through the order of operations to find the value of the variable.
Remember to use inverse operations in order to isolate the variable on one side of the equation.
Whatever you do to one side of an equation, you MUST do to the other side!