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Chapter 2 Section 2.1 Solving Linear Equations

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Isolating the Variable The most common strategy to solve an equation is to isolate the variable. This means to get the variable on one side of the equation (and only one side) all by itself and only numbers on the other side. This is done by doing some group the following to both sides of the equation in the correct order. Add a number or its opposite Multiply by a number or its reciprocal Add an expression or its opposite Combine like terms Distribute numbers into grouping symbols to eliminate the grouping.

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Order of Operations When solving for a variable the order in which you isolate the variable is the opposite of the order of operations. 1)Addition and Subtraction 2)Multiplication, Division and Negative signs 3)Exponents 4)Grouping (Although the first step will be to eliminate the grouping)

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Clearing Fractions If an equation has fractions in it do not try to combine terms with fractions. Get rid of all the fractions by multiplying by a big enough number that will cancel out all of the fractions.

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Variables Cancel Out Sometimes when you try to solve an equation all of the variables will cancel out and leave just numbers. If what is left are two equal numbers the equation is called an identity and all numbers are a solution. If what is left are two unequal numbers the equation is called a contradiction and there is no solution. This is an identity every number will be a solution. This is a contra- diction no number is a solution.

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