Solving Multi-Step equations
To solve a multi step equation, we would start by trying to simplify the equation by combining like terms and using the distributive property whenever possible. First, we will use the distributive property to remove the parenthesis and then we can combine like terms and the isolate the variable. In multi step equations, you will need to make use of the techniques used in solving one step and two step equations. You may want to review those topics before beginning the examples in this lesson.
Just as with solving one step or two-step or any equation, one goal in solving an equation is to have only variables on one side of the equal sign and numbers on the other side of the equal sign. The other goal is to have the number in front of the variable equal to one. Keep in mind that the variable does not always have to be x. These equations can make use of any letter as a variable.
The strategy for getting the variable by itself with a coefficient of 1 involves using opposite operations. For example, to move something that is added to the other side of the equation, you should subtract. The most important thing to remember in solving a linear equation is that whatever you do to one side of the equation, you MUST do to the other side. So if you subtract a number from one side, you MUST subtract the same value from the other side.
We must first put the variables on the same side. Now that we have isolated the variable on the left side of the equation, we can go about solving the new equation using techniques of solving one and two step equations. We must first make sure we have the variable only on one side. It does not matter which side we choose. Some people prefer to always move the variable to the left side while others try to make sure they don't have a negative coefficient. There is no always correct method. The most important thing is to know how to get the variable only on one side. Before we begin to use any of our equation solving skills, we must first simplify the equation by using the distributive property and eliminating the parentheses.
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