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Simplifying 5(3n + -5) + 6(5n + 2) = 5n + 67 Reorder the terms: 5(-5 + 3n) + 6(5n + 2) = 5n + 67 (-5 * 5 + 3n * 5) + 6(5n + 2) = 5n + 67 (-25 + 15n) + 6(5n + 2) = 5n + 67 Reorder the terms: -25 + 15n + 6(2 + 5n) = 5n + 67 -25 + 15n + (2 * 6 + 5n * 6) = 5n + 67 -25 + 15n + (12 + 30n) = 5n + 67 Reorder the terms: -25 + 12 + 15n + 30n = 5n + 67 Combine like terms: -25 + 12 = -13 -13 + 15n + 30n = 5n + 67 Combine like terms: 15n + 30n = 45n -13 + 45n = 5n + 67 Reorder the terms: -13 + 45n = 67 + 5n Solving -13 + 45n = 67 + 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. -13 + 45n + -5n = 67 + 5n + -5n Combine like terms: 45n + -5n = 40n -13 + 40n = 67 + 5n + -5n Combine like terms: 5n + -5n = 0 -13 + 40n = 67 + 0 -13 + 40n = 67 Add '13' to each side of the equation. -13 + 13 + 40n = 67 + 13 Combine like terms: -13 + 13 = 0 0 + 40n = 67 + 13 40n = 67 + 13 Combine like terms: 67 + 13 = 80 40n = 80 Divide each side by '40'. n = 2 Simplifying n = 2
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