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Simplifying 2(n + -2) + 1 = 12 + -1(n + 3) Reorder the terms: 2(-2 + n) + 1 = 12 + -1(n + 3) (-2 * 2 + n * 2) + 1 = 12 + -1(n + 3) (-4 + 2n) + 1 = 12 + -1(n + 3) Reorder the terms: -4 + 1 + 2n = 12 + -1(n + 3) Combine like terms: -4 + 1 = -3 -3 + 2n = 12 + -1(n + 3) Reorder the terms: -3 + 2n = 12 + -1(3 + n) -3 + 2n = 12 + (3 * -1 + n * -1) -3 + 2n = 12 + (-3 + -1n) Combine like terms: 12 + -3 = 9 -3 + 2n = 9 + -1n Solving -3 + 2n = 9 + -1n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add 'n' to each side of the equation. -3 + 2n + n = 9 + -1n + n Combine like terms: 2n + n = 3n -3 + 3n = 9 + -1n + n Combine like terms: -1n + n = 0 -3 + 3n = 9 + 0 -3 + 3n = 9 Add '3' to each side of the equation. -3 + 3 + 3n = 9 + 3 Combine like terms: -3 + 3 = 0 0 + 3n = 9 + 3 3n = 9 + 3 Combine like terms: 9 + 3 = 12 3n = 12 Divide each side by '3'. n = 4 Simplifying n = 4
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