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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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