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