Solving Linear Equations
A linear equation is an equation with two variables that yields a straight line when plotted on a piece of
graph paper. This is one of the most fundamental principles used throughout math courses. Mastering
this topic early on will prove to be helpful later on in your course.
To solve this equation, it is important to known what a “variable,” “constant,” and coefficient” are. A
variable is simple put a symbol for a number we do not know the value of yet. The unknown value is
usually represented by “x” or “y,” but it can be represented by any letter in the alphabet. A variable is
what we solve for in the equation and its value is dependent on the values of the other terms in the
equations. A coefficient is a number in front of the variable and is multiplied by whatever the variable is.
If the term does not have a variable, it is known as a “constant.” The constant has a numerical value that
is both known and set.
For example, in the equation 3x2 + 5x +6 = 0:
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
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x2 and x are the variables.
3 and 5 are the coefficients
and 6 is the constant
So now that we have terms out of the way, let’s work a problem with one variable.
Example:
6x + 2 = 2x + 10. Solve this equation for x.
To solve this equation, begin by moving all terms that contain a variable to one side of the equality sign
and move terms without a variable to the opposite side of the equality side.
6x + 2 = 2x + 10
-2x -2 -2x +2
6x – 2x = 10 – 2
From here, we simplify the variable terms and non-variable terms by adding/subtracting like terms.
4x = 8
To solve for x, we divide both sides of the equation by 4.
4x = 8
4 4
x=2