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Simplifying 5 + 3n + -12 = 2n + 1 Reorder the terms: 5 + -12 + 3n = 2n + 1 Combine like terms: 5 + -12 = -7 -7 + 3n = 2n + 1 Reorder the terms: -7 + 3n = 1 + 2n Solving -7 + 3n = 1 + 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. -7 + 3n + -2n = 1 + 2n + -2n Combine like terms: 3n + -2n = 1n -7 + 1n = 1 + 2n + -2n Combine like terms: 2n + -2n = 0 -7 + 1n = 1 + 0 -7 + 1n = 1 Add '7' to each side of the equation. -7 + 7 + 1n = 1 + 7 Combine like terms: -7 + 7 = 0 0 + 1n = 1 + 7 1n = 1 + 7 Combine like terms: 1 + 7 = 8 1n = 8 Divide each side by '1'. n = 8 Simplifying n = 8
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