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Simplifying 4n + -5(n + 2) = 7 + -3(3 + -1n) Reorder the terms: 4n + -5(2 + n) = 7 + -3(3 + -1n) 4n + (2 * -5 + n * -5) = 7 + -3(3 + -1n) 4n + (-10 + -5n) = 7 + -3(3 + -1n) Reorder the terms: -10 + 4n + -5n = 7 + -3(3 + -1n) Combine like terms: 4n + -5n = -1n -10 + -1n = 7 + -3(3 + -1n) -10 + -1n = 7 + (3 * -3 + -1n * -3) -10 + -1n = 7 + (-9 + 3n) Combine like terms: 7 + -9 = -2 -10 + -1n = -2 + 3n Solving -10 + -1n = -2 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. -10 + -1n + -3n = -2 + 3n + -3n Combine like terms: -1n + -3n = -4n -10 + -4n = -2 + 3n + -3n Combine like terms: 3n + -3n = 0 -10 + -4n = -2 + 0 -10 + -4n = -2 Add '10' to each side of the equation. -10 + 10 + -4n = -2 + 10 Combine like terms: -10 + 10 = 0 0 + -4n = -2 + 10 -4n = -2 + 10 Combine like terms: -2 + 10 = 8 -4n = 8 Divide each side by '-4'. n = -2 Simplifying n = -2
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