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Simplifying 5(3n + 1) = 8(4n + 4) + 7 Reorder the terms: 5(1 + 3n) = 8(4n + 4) + 7 (1 * 5 + 3n * 5) = 8(4n + 4) + 7 (5 + 15n) = 8(4n + 4) + 7 Reorder the terms: 5 + 15n = 8(4 + 4n) + 7 5 + 15n = (4 * 8 + 4n * 8) + 7 5 + 15n = (32 + 32n) + 7 Reorder the terms: 5 + 15n = 32 + 7 + 32n Combine like terms: 32 + 7 = 39 5 + 15n = 39 + 32n Solving 5 + 15n = 39 + 32n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-32n' to each side of the equation. 5 + 15n + -32n = 39 + 32n + -32n Combine like terms: 15n + -32n = -17n 5 + -17n = 39 + 32n + -32n Combine like terms: 32n + -32n = 0 5 + -17n = 39 + 0 5 + -17n = 39 Add '-5' to each side of the equation. 5 + -5 + -17n = 39 + -5 Combine like terms: 5 + -5 = 0 0 + -17n = 39 + -5 -17n = 39 + -5 Combine like terms: 39 + -5 = 34 -17n = 34 Divide each side by '-17'. n = -2 Simplifying n = -2
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