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Simplifying -1(7 + -5(1 + -1n)) + 8n = -24 + 5(6(n + 1) + -3n) -1(7 + (1 * -5 + -1n * -5)) + 8n = -24 + 5(6(n + 1) + -3n) -1(7 + (-5 + 5n)) + 8n = -24 + 5(6(n + 1) + -3n) Combine like terms: 7 + -5 = 2 -1(2 + 5n) + 8n = -24 + 5(6(n + 1) + -3n) (2 * -1 + 5n * -1) + 8n = -24 + 5(6(n + 1) + -3n) (-2 + -5n) + 8n = -24 + 5(6(n + 1) + -3n) Combine like terms: -5n + 8n = 3n -2 + 3n = -24 + 5(6(n + 1) + -3n) Reorder the terms: -2 + 3n = -24 + 5(6(1 + n) + -3n) -2 + 3n = -24 + 5((1 * 6 + n * 6) + -3n) -2 + 3n = -24 + 5((6 + 6n) + -3n) Combine like terms: 6n + -3n = 3n -2 + 3n = -24 + 5(6 + 3n) -2 + 3n = -24 + (6 * 5 + 3n * 5) -2 + 3n = -24 + (30 + 15n) Combine like terms: -24 + 30 = 6 -2 + 3n = 6 + 15n Solving -2 + 3n = 6 + 15n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-15n' to each side of the equation. -2 + 3n + -15n = 6 + 15n + -15n Combine like terms: 3n + -15n = -12n -2 + -12n = 6 + 15n + -15n Combine like terms: 15n + -15n = 0 -2 + -12n = 6 + 0 -2 + -12n = 6 Add '2' to each side of the equation. -2 + 2 + -12n = 6 + 2 Combine like terms: -2 + 2 = 0 0 + -12n = 6 + 2 -12n = 6 + 2 Combine like terms: 6 + 2 = 8 -12n = 8 Divide each side by '-12'. n = -0.6666666667 Simplifying n = -0.6666666667
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