**Linear equations may be solved by isolating the variable or variables.** Solving linear equations involves undoing whatever operations have been done to the variable and putting the variable alone on one side of the equal sign.

A linear equation describes a straight line. In a simple linear equation, operations can be undone by performing the same operation to both sides. For the equation x + 3 = 10, the +3 can be undone by subtracting the same number, 3, from both sides of the equation.

- x + 3 - 3 = 10 - 3
- x = 7

Where there is more than one operation performed on the variable, they must be undone in a specific order: addition and subtraction before multiplication and division. The equation 3x + 4 = 10, therefore, involves four steps.

- 3x + 4 - 4 = 10 - 4
- 3x = 6
- 3x/3 = 6/3
- x = 2

Other variations may include variables on both sides of the equation or fractions in the equation. In all cases, the basic method remains the same: isolate the variable on one side of the equal sign, balancing out the equation by performing the same operation(s) to both sides. For example, for the equation 6x + 4 - 2x + 1 = 2x + 3:

- Simplify the left side: 4x + 5 = 2x + 3
- 4x + 5 - 5 = 2x + 3 - 5
- 4x = 2x - 2
- 2x = -2
- x = -1