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Simplifying -7(6n + 7) = 31 + -2n Reorder the terms: -7(7 + 6n) = 31 + -2n (7 * -7 + 6n * -7) = 31 + -2n (-49 + -42n) = 31 + -2n Solving -49 + -42n = 31 + -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. -49 + -42n + 2n = 31 + -2n + 2n Combine like terms: -42n + 2n = -40n -49 + -40n = 31 + -2n + 2n Combine like terms: -2n + 2n = 0 -49 + -40n = 31 + 0 -49 + -40n = 31 Add '49' to each side of the equation. -49 + 49 + -40n = 31 + 49 Combine like terms: -49 + 49 = 0 0 + -40n = 31 + 49 -40n = 31 + 49 Combine like terms: 31 + 49 = 80 -40n = 80 Divide each side by '-40'. n = -2 Simplifying n = -2
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