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Simplifying 3n + -5 + n + -8 = -4(-8n + 4) + -5(1 + 4n) Reorder the terms: -5 + -8 + 3n + n = -4(-8n + 4) + -5(1 + 4n) Combine like terms: -5 + -8 = -13 -13 + 3n + n = -4(-8n + 4) + -5(1 + 4n) Combine like terms: 3n + n = 4n -13 + 4n = -4(-8n + 4) + -5(1 + 4n) Reorder the terms: -13 + 4n = -4(4 + -8n) + -5(1 + 4n) -13 + 4n = (4 * -4 + -8n * -4) + -5(1 + 4n) -13 + 4n = (-16 + 32n) + -5(1 + 4n) -13 + 4n = -16 + 32n + (1 * -5 + 4n * -5) -13 + 4n = -16 + 32n + (-5 + -20n) Reorder the terms: -13 + 4n = -16 + -5 + 32n + -20n Combine like terms: -16 + -5 = -21 -13 + 4n = -21 + 32n + -20n Combine like terms: 32n + -20n = 12n -13 + 4n = -21 + 12n Solving -13 + 4n = -21 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. -13 + 4n + -12n = -21 + 12n + -12n Combine like terms: 4n + -12n = -8n -13 + -8n = -21 + 12n + -12n Combine like terms: 12n + -12n = 0 -13 + -8n = -21 + 0 -13 + -8n = -21 Add '13' to each side of the equation. -13 + 13 + -8n = -21 + 13 Combine like terms: -13 + 13 = 0 0 + -8n = -21 + 13 -8n = -21 + 13 Combine like terms: -21 + 13 = -8 -8n = -8 Divide each side by '-8'. n = 1 Simplifying n = 1
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