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Simplifying 5(1 + -3n) + 7 = 7(n + 8) (1 * 5 + -3n * 5) + 7 = 7(n + 8) (5 + -15n) + 7 = 7(n + 8) Reorder the terms: 5 + 7 + -15n = 7(n + 8) Combine like terms: 5 + 7 = 12 12 + -15n = 7(n + 8) Reorder the terms: 12 + -15n = 7(8 + n) 12 + -15n = (8 * 7 + n * 7) 12 + -15n = (56 + 7n) Solving 12 + -15n = 56 + 7n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-7n' to each side of the equation. 12 + -15n + -7n = 56 + 7n + -7n Combine like terms: -15n + -7n = -22n 12 + -22n = 56 + 7n + -7n Combine like terms: 7n + -7n = 0 12 + -22n = 56 + 0 12 + -22n = 56 Add '-12' to each side of the equation. 12 + -12 + -22n = 56 + -12 Combine like terms: 12 + -12 = 0 0 + -22n = 56 + -12 -22n = 56 + -12 Combine like terms: 56 + -12 = 44 -22n = 44 Divide each side by '-22'. n = -2 Simplifying n = -2
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