124 Chapter 2 Linear Equations and Inequalities Answer 4. {1} Solving a Linear Equation Containing Fractions Solve the equation. Solution: The LCD of and is 10. Multiply both sides by 10. Apply the distributive property. Clear fractions. Apply the distributive property. Simplify both sides of the equation. Subtract 16 from both sides. x 2 5 5 21x 22 51x 42 20 2x 4 5x 20 20 3x 16 20 3x 16 16 20 16 3x 4 Divide both sides by 3. The check is left to the reader. 10 The solution set is e 4 3 Skill Practice Solve the equation. 4. x 1 4 x 2 6 1 f . x 4 3 3x 3 4 3 2 1 a x 2 5 b 10 1 a x 4 2 b 10 1 a 2 1 b 10a x 2 5 x 4 2 b 10 a 2 1 b 21 x 2 5 , x 4 2 , x 4 2 2 1 x 2 5 x 4 2 2 Example 4 2. Linear Equations Containing Decimals The same procedure used to clear fractions in an equation can be used to clear decimals. For example, consider the equation 2.5x 3 1.7x 6.6 Recall that any terminating decimal can be written as a fraction. Therefore, the equation can be interpreted as 25 10 x 3 17 10 x 66 10 A convenient common denominator of all terms is 10.Therefore, we can multiply the original equation by 10 to clear decimals.The result is 25x 30 17x 66 Multiplying by the appropriate power of 10 moves the decimal points so that all coefficients become integers. Avoiding Mistakes In Example 4, several of the fractions in the equation have two terms in the numerator. It is important to enclose these fractions in parentheses when clearing fractions. In this way, we will remember to use the distributive property to multiply the factors shown in blue with both terms from the numerator of the fractions.
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