106 Chapter 2 Linear Equations and Inequalities in One Variable Check: 3(x + 2) - (2x - 5) = 0 Original equation 3(-11 + 2) - 2(-11) - 5 = 0 Replace x with -11. 3(-9) - (-22 - 5) = 0 Simplify the left side using the -27 - (-27) = 0 order of operations. -27 + 27 = 0 Add. 0 = 0 Simplify. Since x = -11 makes the equation true, the solution set is {-11}. 3e. 3(x + 6) = 4(x - 1) 3x + 18 = 4x - 4 Apply the distributive property. 3x + 18 - 3x = 4x - 4 - 3x Subtract 3x from each side. 18 = x -4 Simplify. 18 + 4 = x - 4 + 4 Add 4 to each side. 22 = x Simplify. Check: 3 (x + 6) = 4(x - 1) Original equation 3(22 + 6) = 4(22 - 1) Replace x with 22. 3(28) = 4(21) Simplify each side. 84 = 84 Multiply. Since x = 22 makes the equation true, the solution set is {22}. Student Check 3 Solve each equation. a. -3t + 5 + 4t = 0 b. 0.2y + 6 - 3 + 0.8y = 0 c. 5t - 1 = 4t + 4 d. 2(x - 5) - (x + 3) = 5 e. 5(x + 2) = 4(x - 1) Applications The key to solving applications is setting up the equation correctly. In Section 2.1, we practiced setting up the equation but not solving them. Feel free to go back and review this material as needed. The only difference in what we are doing in this section is that we will solve the equation we set up. �� ������������������������ ������������������ For each problem: (1) assign a variable to the unknown, (2) write an equation that represents the situation, (3) solve the equation, and (4) answer the question using complete sentences. 4a. Four less than twice a number has the same result as eight more than a number. Find the number. Solution 4a. What is the unknown? The number is unknown. Let n be a number. What is known? Four less than twice a number has the same result as eight more than a number. Objective 4 ▶ Solve applications of linear equations.
hendricks_beginning_algebra_1e_ch1_3
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