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Simplifying 3 + 4n + -1(5n + 7) = 2(n + -3) + 5 Reorder the terms: 3 + 4n + -1(7 + 5n) = 2(n + -3) + 5 3 + 4n + (7 * -1 + 5n * -1) = 2(n + -3) + 5 3 + 4n + (-7 + -5n) = 2(n + -3) + 5 Reorder the terms: 3 + -7 + 4n + -5n = 2(n + -3) + 5 Combine like terms: 3 + -7 = -4 -4 + 4n + -5n = 2(n + -3) + 5 Combine like terms: 4n + -5n = -1n -4 + -1n = 2(n + -3) + 5 Reorder the terms: -4 + -1n = 2(-3 + n) + 5 -4 + -1n = (-3 * 2 + n * 2) + 5 -4 + -1n = (-6 + 2n) + 5 Reorder the terms: -4 + -1n = -6 + 5 + 2n Combine like terms: -6 + 5 = -1 -4 + -1n = -1 + 2n Solving -4 + -1n = -1 + 2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2n' to each side of the equation. -4 + -1n + -2n = -1 + 2n + -2n Combine like terms: -1n + -2n = -3n -4 + -3n = -1 + 2n + -2n Combine like terms: 2n + -2n = 0 -4 + -3n = -1 + 0 -4 + -3n = -1 Add '4' to each side of the equation. -4 + 4 + -3n = -1 + 4 Combine like terms: -4 + 4 = 0 0 + -3n = -1 + 4 -3n = -1 + 4 Combine like terms: -1 + 4 = 3 -3n = 3 Divide each side by '-3'. n = -1 Simplifying n = -1
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