To solve multi-step equations in algebra, you need to collect like terms, simplify the expressions and follow the order of operations to isolate the variable. Following the order of operations is vital, because other methods generally give incorrect results.
- Combine all like terms
Like terms in an expression are terms that feature the same variable and the same degree. For example, 5x and 3x are like terms, while 6x and 3y or 5x^2 and 3x are not. For practice, work with the equation 3(x + 5) + 4x + 6 - 5x = 3x - 2. On the left side, 4x and -5x can be added to yield -x. If you use the distributive property, 3(x + 5) converts to 3x + 15, leaving 3x, 4x and -5x as like terms on the left side of the equation.
- Follow the order of operations as necessary
The order of operations is parentheses, exponents, division, multiplication, addition then subtraction. The equation in the example now reads 2x + 21 = 3x - 2.
- Isolate the variable
In the example, add 2 to both sides of the equation, leaving you with 2x + 23 = 3x. Subtract 2x from both sides. This yields 23 = x. Substitute 23 into the original equation to verify that it works.