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Simplifying 15n + -20(1 + 30n) = -34 + -23(19n + 38) 15n + (1 * -20 + 30n * -20) = -34 + -23(19n + 38) 15n + (-20 + -600n) = -34 + -23(19n + 38) Reorder the terms: -20 + 15n + -600n = -34 + -23(19n + 38) Combine like terms: 15n + -600n = -585n -20 + -585n = -34 + -23(19n + 38) Reorder the terms: -20 + -585n = -34 + -23(38 + 19n) -20 + -585n = -34 + (38 * -23 + 19n * -23) -20 + -585n = -34 + (-874 + -437n) Combine like terms: -34 + -874 = -908 -20 + -585n = -908 + -437n Solving -20 + -585n = -908 + -437n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '437n' to each side of the equation. -20 + -585n + 437n = -908 + -437n + 437n Combine like terms: -585n + 437n = -148n -20 + -148n = -908 + -437n + 437n Combine like terms: -437n + 437n = 0 -20 + -148n = -908 + 0 -20 + -148n = -908 Add '20' to each side of the equation. -20 + 20 + -148n = -908 + 20 Combine like terms: -20 + 20 = 0 0 + -148n = -908 + 20 -148n = -908 + 20 Combine like terms: -908 + 20 = -888 -148n = -888 Divide each side by '-148'. n = 6 Simplifying n = 6
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