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Simplifying 4(n + -5) + 5(-3n + -2) = 47 Reorder the terms: 4(-5 + n) + 5(-3n + -2) = 47 (-5 * 4 + n * 4) + 5(-3n + -2) = 47 (-20 + 4n) + 5(-3n + -2) = 47 Reorder the terms: -20 + 4n + 5(-2 + -3n) = 47 -20 + 4n + (-2 * 5 + -3n * 5) = 47 -20 + 4n + (-10 + -15n) = 47 Reorder the terms: -20 + -10 + 4n + -15n = 47 Combine like terms: -20 + -10 = -30 -30 + 4n + -15n = 47 Combine like terms: 4n + -15n = -11n -30 + -11n = 47 Solving -30 + -11n = 47 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + -11n = 47 + 30 Combine like terms: -30 + 30 = 0 0 + -11n = 47 + 30 -11n = 47 + 30 Combine like terms: 47 + 30 = 77 -11n = 77 Divide each side by '-11'. n = -7 Simplifying n = -7
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