Article: The simplest algebraic equations, those involving just a few variable terms with whole number coefficients and no fractions, radicals, etc., can often be solved in just a few steps. As with most math problems, the first step to simplifying your equation is to write it out! As an example problem, for the next few steps, let's consider the expression 1 + 2x - 3 + 4x. Next, search your equation for like terms. Remember that like terms have both the same variable(s) and exponent(s). For example, let's identify like terms in our equation 1 + 2x - 3 + 4x. 2x and 4x both have the same variable raised to the same exponent (in this case, the x's aren't raised to any exponent at all). In addition, 1 and -3 are like terms, as neither has any variables. So, in our equation, 2x and 4x and 1 and -3 are like terms. Now that you've identified like terms, you can combine them to simplify your equation. Add terms together (or subtract in the case of negative terms) to reduce each set of terms with the same variables and exponents to one singular term. Let's add the like terms in our example. 2x + 4x = 6x 1 + -3 = -2 After combining your like terms, construct an expression from your new, smaller set of terms. You should get a simpler expression that has one term for each different set of variables and exponents in the original expression. This new expression is equal to the first. In our example, our simplified terms are 6x and -2, so our new expression is 6x - 2. This simplified expression is equal to the original (1 + 2x - 3 + 4x), but is shorter and easier to manage. It's also easier to factor, which, as we'll see below, is another important simplifying skill. In extremely simple expressions like the one dealt with in the example problems above, identifying like terms is simple. However, in more complex expressions, like ones that involve terms in parentheses, fractions, and radicals, like terms which can be combined may not be immediately apparent. In these cases, follow the order of operations, performing operations on the terms in your expression as necessary until only addition and subtraction operations remain. For example, let's consider the equation 5(3x-1) + x((2x)/(2)) + 8 - 3x. It would be incorrect to immediately identify 3x and 2x as like terms and combine them because the parentheses in the expression dictate that we're supposed to do other operations first. First, let's perform the arithmetic operations in the expression in accordance with the order of operations to obtain terms we can use. See below: 5(3x-1) + x((2x)/(2)) + 8 - 3x 15x - 5 + x(x) + 8 - 3x 15x - 5 + x2 + 8 - 3x. Now, since the only operations left are addition and subtraction, we can combine like terms. x2 + (15x - 3x) + (8 - 5) x2 + 12x + 3

What is a summary?
Write your equation. Identify like terms. Combine like terms. Create a simplified expression from your simplified terms. Obey the order of operation when combining like terms.