200 Chapter 2 Linear Equations and Inequalities Linear Equations: Clearing Fractions and Decimals Section 2.3 Key Concepts Steps for Solving a Linear Equation in One Variable: 1. Simplify both sides of the equation. • Clear parentheses • Consider clearing fractions or decimals (if any are present) by multiplying both sides of the equation by a common denominator of all terms • Combine like terms 2. Use the addition or subtraction property of equality to collect the variable terms on one side of the equation. 3. Use the addition or subtraction property of equality to collect the constant terms on the other side of the equation. 4. Use the multiplication or division property of equality to make the coefficient of the variable term equal to 1. 5. Check your answer. Examples Example 1 Multiply by the LCD. Apply distributive property. Combine like terms. Add 8 to both sides. Divide by 1 2 x 2 x 2 3 4 3 4 x xb 7 4 4 1 2x 8 3x 7 x 8 7 a7 4b x 15 x 15 1. 4 1 a1 2 The solution 15 checks in the original equation. Example 2 Multiply both sides by 10. 1.2x 5.1 16.5 1011.2x 5.12 10116.52 12x 51 165 12x 216 12x 12 216 12 x 18 The solution 18 checks in the original equation.
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