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Simplifying 5(n + -12) + -24 = 3(n + 2) Reorder the terms: 5(-12 + n) + -24 = 3(n + 2) (-12 * 5 + n * 5) + -24 = 3(n + 2) (-60 + 5n) + -24 = 3(n + 2) Reorder the terms: -60 + -24 + 5n = 3(n + 2) Combine like terms: -60 + -24 = -84 -84 + 5n = 3(n + 2) Reorder the terms: -84 + 5n = 3(2 + n) -84 + 5n = (2 * 3 + n * 3) -84 + 5n = (6 + 3n) Solving -84 + 5n = 6 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. -84 + 5n + -3n = 6 + 3n + -3n Combine like terms: 5n + -3n = 2n -84 + 2n = 6 + 3n + -3n Combine like terms: 3n + -3n = 0 -84 + 2n = 6 + 0 -84 + 2n = 6 Add '84' to each side of the equation. -84 + 84 + 2n = 6 + 84 Combine like terms: -84 + 84 = 0 0 + 2n = 6 + 84 2n = 6 + 84 Combine like terms: 6 + 84 = 90 2n = 90 Divide each side by '2'. n = 45 Simplifying n = 45
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