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Chapter 13

Solving Linear Equations

Linear equations are of the form , where x is some variable, and a, b, and c are real numbers. To solve a linear equation, you perform a series of opposites: If a number is added to the term containing x, you subtract that number from both sides of the equation; if a number is subtracted from the term containing the variable, you add; if a number multiplies the variable, you divide; and if a number divides the variable, you multiply. Just be sure that whatever you do to one side of the equation, you also do to the other side. Think of the equation as two expressions pivoting on either side of a balance scale — you need to keep the sides evenly balanced.

The Problems You’ll Work On

Here are a few things you do in this chapter to find answers:

 Using the addition property to solve linear equations

 Using multiplication and division — inverses of one another — to solve linear equations

 Combining operations — doing more than one operation for a solution

 Rewriting equations by eliminating grouping symbols

 Getting rid of fractions and fractional expressions before solving linear equations

What to Watch Out For

As you get in a groove solving linear equations, be sure you’re doing the following:

 Performing the same operation on each side of the equation to keep it balanced

 Being careful to use the inverse/opposite number when adding and subtracting

 Never multiplying or dividing by 0

 Distributing correctly to remove grouping symbols, especially with negative numbers

Solving Linear Equations Using Basic Operations

566–583 Solve the linear equations for the value of the variable.

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Dealing with Fractions in Linear Equations

584–605 Solve for the value of the variable by eliminating the fraction.

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