What is a linear equation in one variable? Definition and examples


A linear equation in one variable is an equation that have the same solution as the equation of the form ax + b = 0, where a and b are integers and a is not equal to zero.

In other words, if an equation can be written in the form ax + b = 0, then it is a linear equation in 1 variable.

In ax + b = 0, a is a coefficient, b is a constant, and x is a variable

Notice that the following are true for the variable x

  • x is the only variable in a linear equation in one variable
  • x is unknown
  • x cannot be raised to a power other than 1
  • x has only one solution

For example, 5x + 2 = 3x + 6 is a linear equation in one variable since it is possible to write it in the form ax + b = 0 using some of the properties of equality.

5x + 2 = 3x - 4

5x + 2 + 4 = 3x - 4 + 4  (addition property of equality)

5x + 6 = 3x 

5x - 3x + 6 = 3x - 3x (subtraction property of equality)

2x + 6 = 0

Since 5x + 2 = 3x + 6 can be written as 2x + 6 = 0, it is a linear equation 

More examples of linear equations in one variable

6x + 2 = 20

4x - 5 = 12 + - 5 

2x - 8 + 6 = 7

-x + 5 = 4x

100 + 100x = 200 + 300

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