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Simplifying 15 = 2[n + (n + 1)] + -1[(n + 2) + (n + 3)] Reorder the terms: 15 = 2[n + (1 + n)] + -1[(n + 2) + (n + 3)] Remove parenthesis around (1 + n) 15 = 2[n + 1 + n] + -1[(n + 2) + (n + 3)] Reorder the terms: 15 = 2[1 + n + n] + -1[(n + 2) + (n + 3)] Combine like terms: n + n = 2n 15 = 2[1 + 2n] + -1[(n + 2) + (n + 3)] 15 = [1 * 2 + 2n * 2] + -1[(n + 2) + (n + 3)] 15 = [2 + 4n] + -1[(n + 2) + (n + 3)] Reorder the terms: 15 = 2 + 4n + -1[(2 + n) + (n + 3)] Remove parenthesis around (2 + n) 15 = 2 + 4n + -1[2 + n + (n + 3)] Reorder the terms: 15 = 2 + 4n + -1[2 + n + (3 + n)] Remove parenthesis around (3 + n) 15 = 2 + 4n + -1[2 + n + 3 + n] Reorder the terms: 15 = 2 + 4n + -1[2 + 3 + n + n] Combine like terms: 2 + 3 = 5 15 = 2 + 4n + -1[5 + n + n] Combine like terms: n + n = 2n 15 = 2 + 4n + -1[5 + 2n] 15 = 2 + 4n + [5 * -1 + 2n * -1] 15 = 2 + 4n + [-5 + -2n] Reorder the terms: 15 = 2 + -5 + 4n + -2n Combine like terms: 2 + -5 = -3 15 = -3 + 4n + -2n Combine like terms: 4n + -2n = 2n 15 = -3 + 2n Solving 15 = -3 + 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. 15 + -2n = -3 + 2n + -2n Combine like terms: 2n + -2n = 0 15 + -2n = -3 + 0 15 + -2n = -3 Add '-15' to each side of the equation. 15 + -15 + -2n = -3 + -15 Combine like terms: 15 + -15 = 0 0 + -2n = -3 + -15 -2n = -3 + -15 Combine like terms: -3 + -15 = -18 -2n = -18 Divide each side by '-2'. n = 9 Simplifying n = 9
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