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Simplifying 3[10 + (3n + -1) + -1(4 + -1n)] = 5(n + 10) Reorder the terms: 3[10 + (-1 + 3n) + -1(4 + -1n)] = 5(n + 10) Remove parenthesis around (-1 + 3n) 3[10 + -1 + 3n + -1(4 + -1n)] = 5(n + 10) 3[10 + -1 + 3n + (4 * -1 + -1n * -1)] = 5(n + 10) 3[10 + -1 + 3n + (-4 + 1n)] = 5(n + 10) Reorder the terms: 3[10 + -1 + -4 + 3n + 1n] = 5(n + 10) Combine like terms: 10 + -1 = 9 3[9 + -4 + 3n + 1n] = 5(n + 10) Combine like terms: 9 + -4 = 5 3[5 + 3n + 1n] = 5(n + 10) Combine like terms: 3n + 1n = 4n 3[5 + 4n] = 5(n + 10) [5 * 3 + 4n * 3] = 5(n + 10) [15 + 12n] = 5(n + 10) Reorder the terms: 15 + 12n = 5(10 + n) 15 + 12n = (10 * 5 + n * 5) 15 + 12n = (50 + 5n) Solving 15 + 12n = 50 + 5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5n' to each side of the equation. 15 + 12n + -5n = 50 + 5n + -5n Combine like terms: 12n + -5n = 7n 15 + 7n = 50 + 5n + -5n Combine like terms: 5n + -5n = 0 15 + 7n = 50 + 0 15 + 7n = 50 Add '-15' to each side of the equation. 15 + -15 + 7n = 50 + -15 Combine like terms: 15 + -15 = 0 0 + 7n = 50 + -15 7n = 50 + -15 Combine like terms: 50 + -15 = 35 7n = 35 Divide each side by '7'. n = 5 Simplifying n = 5
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