Summary 199 Section 2.2 Solving Linear Equations Key Concepts Steps for Solving a Linear Equation in One Variable: 1. Simplify both sides of the equation. • Clear parentheses • 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. A conditional equation is true for some values of the variable but is false for other values. An equation that has all real numbers as its solution set is an identity. An equation that has no solution is a contradiction. Examples Example 1 Clear parentheses. Combine like terms. Collect the variable terms. Collect the constant terms. Divide both sides by 2. Check: 5142 7 33142 14 2 20 7 3152 2 13 15 2 ✔ True 5y 7 31y 12 2 5y 7 3y 3 2 5y 7 3y 1 2y 7 1 2y 8 Example 2 is a conditional equation because it is true only on the condition that . Example 3 x 4 21x 22 x x 4 2x 4 x x 4 x 4 4 4 is an identity The solution is all real numbers. Example 4 y 5 21y 32 y y 5 2y 6 y y 5 y 6 5 6 is a contradiction There is no solution. x 2 x 5 7 13 13 y 4 The solution is 4.
miller_introductory_algebra_3e_ch1_3
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