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Simplifying -3n + -7(2n + -1) = 45 + -3(4n + 1) Reorder the terms: -3n + -7(-1 + 2n) = 45 + -3(4n + 1) -3n + (-1 * -7 + 2n * -7) = 45 + -3(4n + 1) -3n + (7 + -14n) = 45 + -3(4n + 1) Reorder the terms: 7 + -3n + -14n = 45 + -3(4n + 1) Combine like terms: -3n + -14n = -17n 7 + -17n = 45 + -3(4n + 1) Reorder the terms: 7 + -17n = 45 + -3(1 + 4n) 7 + -17n = 45 + (1 * -3 + 4n * -3) 7 + -17n = 45 + (-3 + -12n) Combine like terms: 45 + -3 = 42 7 + -17n = 42 + -12n Solving 7 + -17n = 42 + -12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '12n' to each side of the equation. 7 + -17n + 12n = 42 + -12n + 12n Combine like terms: -17n + 12n = -5n 7 + -5n = 42 + -12n + 12n Combine like terms: -12n + 12n = 0 7 + -5n = 42 + 0 7 + -5n = 42 Add '-7' to each side of the equation. 7 + -7 + -5n = 42 + -7 Combine like terms: 7 + -7 = 0 0 + -5n = 42 + -7 -5n = 42 + -7 Combine like terms: 42 + -7 = 35 -5n = 35 Divide each side by '-5'. n = -7 Simplifying n = -7
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