Here's a useful math lesson plan for teachers covering linear equations. You'll find definitions and examples of how to solve problems that you can use with your students.
What is an Equation?
An equation is a mathematical statement stating the equality of two mathematical expressions. An equation is usually written as a meaningful linear array of mathematical symbols that has left and right sides and is connected by an equal sign.
(x - 3)/2=7 is an equation but ) x (3-/2=7 is not because in the second example, the mathematical symbols do not form a meaningful linear array.
What is a Linear Equation?
A linear equation is an equation in which the highest exponent of the variable / variables is 1. For example (x-3)/2=7 is a linear equation but (x2 -3)/2=7 is not because the power of x is 2. It is called “linear" because the graph between any of the two variables will be a straight line. In the second example, because negative numbers squared are the same as the positive counterpart squared, make two x-coordinate values for each y.
When teaching linear equations, remind students that for a linear equation to be true, the left side must be equal to the right side.
Fundamentals for Solving and Teaching Linear Equations
The Equality Property for Addition and Subtraction: If two expressions are equal then adding or subtracting equal numbers to both sides does not change that equality.
For example, If m = n then, m+c = n+c and m-d = n-d
The Equality Property for Multiplication and Division: If two expressions are equal then multiplying or dividing by any equal number except zero on both sides does not change that equality.
For example, if m=n then, m/c = n/c and m x d = n x d where c is not equal to zero.
The Rule of Inverse: Addition and subtraction are inverse to each other, which means if some number is added to one side of a linear equation and you want to take it to the other side then you have to subtract the number from both sides.
For example, in the equation x – 3 = 7 if you want to take 3 to the right side then you have to add both the side with 3 and the linear equation will become x = 10.
Similarly, multiplication and division are inverse to each other.
For example, (x – 3)/2 = 7 here we can take 2 on the right hand side by multiplying both sides by 2.
Solving a Linear Equation with One Variable
Simplify: 1. Remove fractions by multiplying both sides of the linear equation by the denominator.
2. Use the distributive property to remove parenthesis.
Use equality properties: Use equality properties for addition/subtraction and multiplication/division to move numbers (constants) to one side.
(x – 3)/2 = 7
or, x/2 – 3/2 = 7 (using distributive property for removing parenthesis)
or, x – 3 = 14 (using equality property for multiplication/division and multiplying by 2 on both the sides)
or, x = 17 (using equality property for addition/subtraction and adding 3 on both the sides)