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Simplifying 3(n + -2) + -1 = 2 + -5(n + 5) Reorder the terms: 3(-2 + n) + -1 = 2 + -5(n + 5) (-2 * 3 + n * 3) + -1 = 2 + -5(n + 5) (-6 + 3n) + -1 = 2 + -5(n + 5) Reorder the terms: -6 + -1 + 3n = 2 + -5(n + 5) Combine like terms: -6 + -1 = -7 -7 + 3n = 2 + -5(n + 5) Reorder the terms: -7 + 3n = 2 + -5(5 + n) -7 + 3n = 2 + (5 * -5 + n * -5) -7 + 3n = 2 + (-25 + -5n) Combine like terms: 2 + -25 = -23 -7 + 3n = -23 + -5n Solving -7 + 3n = -23 + -5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5n' to each side of the equation. -7 + 3n + 5n = -23 + -5n + 5n Combine like terms: 3n + 5n = 8n -7 + 8n = -23 + -5n + 5n Combine like terms: -5n + 5n = 0 -7 + 8n = -23 + 0 -7 + 8n = -23 Add '7' to each side of the equation. -7 + 7 + 8n = -23 + 7 Combine like terms: -7 + 7 = 0 0 + 8n = -23 + 7 8n = -23 + 7 Combine like terms: -23 + 7 = -16 8n = -16 Divide each side by '8'. n = -2 Simplifying n = -2
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