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