Section 2.3 Linear Equations: Clearing Fractions and Decimals 125 TIP: Notice that multiplying a decimal number by 10 has the effect of moving the decimal point one place to the right. Similarly, multiplying by 100 moves the decimal point two places to the right, and so on. Answers 5. 576 6. 539.56 Solving a Linear Equation Containing Decimals Solve the equation by clearing decimals. Solution: Multiply both sides of the equation by 10. Apply the distributive property. Subtract 17x from both sides. Subtract 30 from both sides. Divide both sides by 8. The check is left to the reader. 2.5x 3 1.7x 6.6 1012.5x 32 1011.7x 6.62 25x 30 17x 66 25x 17x 30 17x 17x 66 8x 30 66 8x 30 30 66 30 8x 96 8x 8 96 8 x 12 The solution set is {12}. Skill Practice Solve the equation. 5. 1.2w 3.5 2.1 w 2.5x 3 1.7x 6.6 Example 5 Solving a Linear Equation Containing Decimals Solve the equation by clearing decimals. Solution: Clear parentheses first. Multiply both sides by 100. Apply the distributive property. Simplify both sides. Add 325 to both sides. Divide both sides by The check is left to the reader. 0.21x 42 0.451x 92 12 0.2x 0.8 0.45x 4.05 12 10010.2x 0.8 0.45x 4.052 1001122 20x 80 45x 405 1200 25x 325 1200 25x 325 325 1200 325 25x 1525 x 61 The solution set is {61}. Skill Practice Solve the equation. 6. 0.251x 22 0.15 1x 32 4 25. 25x 25 1525 25 0.21x 42 0.451x 92 12 Example 6 TIP: The terms with the most digits following the decimal point are 0.45x and 4.05. Each of these is written to the hundredths place. Therefore, we multiply both sides by 100.
miller_beginning_intermediate_algebra_4e_ch1_3
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