- 1). Move the variables to one side of the equation and the integers to the other. This will greatly simplify the problem and enable you to solve it quickly and easily. To isolate the variables from the integers, use addition and subtraction. Remember, any operation -- addition or subtraction -- you perform on one side of the equation you must also perform on the other. For example, if you wish to solve the equation 6x + 2 = 3x -1, you can subtract 3x and 2 from both sides; this leaves you with the equation 3x = -3.
- 2). Divide both sides of the equation by the coefficient in front of the variable. The idea here is to find the value of "x" by isolating it. In the example, you know what 3x equals; dividing by the coefficient in front of the variable allows you to know the value of 1x (or simply x). In the example, 3x = -3, divide both sides by 3. This leaves you with x = -1. Now you know the value of variable "x."
- 3). Check your work for accuracy by running the solution through the original equation. Now that you know what the variable stands for, go back to the original equation and plug in the integer for each variable that you see. If the equation remains true after the substitution, you have correctly solved for the variable. In the example given, 6x + 2 = 3X -1 , plug in -1 for each "x" you see. This will give you 6(-1) + 2 = 3(-1) - 1. This simplifies to -6 + 2 = -3 -1, which simplifies further to -4=-4, which is true. Because it simplifies to a true statement, the value for "x" must be correct.
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