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Simplifying 2[7 + -7(1 + -1n)] + 5n = -22 + 4[6(n + 1) + -3n] 2[7 + (1 * -7 + -1n * -7)] + 5n = -22 + 4[6(n + 1) + -3n] 2[7 + (-7 + 7n)] + 5n = -22 + 4[6(n + 1) + -3n] Combine like terms: 7 + -7 = 0 2[0 + 7n] + 5n = -22 + 4[6(n + 1) + -3n] 2[7n] + 5n = -22 + 4[6(n + 1) + -3n] Remove brackets around [7n] 2 * 7n + 5n = -22 + 4[6(n + 1) + -3n] Multiply 2 * 7 14n + 5n = -22 + 4[6(n + 1) + -3n] Combine like terms: 14n + 5n = 19n 19n = -22 + 4[6(n + 1) + -3n] Reorder the terms: 19n = -22 + 4[6(1 + n) + -3n] 19n = -22 + 4[(1 * 6 + n * 6) + -3n] 19n = -22 + 4[(6 + 6n) + -3n] Combine like terms: 6n + -3n = 3n 19n = -22 + 4[6 + 3n] 19n = -22 + [6 * 4 + 3n * 4] 19n = -22 + [24 + 12n] Combine like terms: -22 + 24 = 2 19n = 2 + 12n Solving 19n = 2 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. 19n + -12n = 2 + 12n + -12n Combine like terms: 19n + -12n = 7n 7n = 2 + 12n + -12n Combine like terms: 12n + -12n = 0 7n = 2 + 0 7n = 2 Divide each side by '7'. n = 0.2857142857 Simplifying n = 0.2857142857
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