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Simplifying 7(3n + 1) = 9(5n + 2) + 4 Reorder the terms: 7(1 + 3n) = 9(5n + 2) + 4 (1 * 7 + 3n * 7) = 9(5n + 2) + 4 (7 + 21n) = 9(5n + 2) + 4 Reorder the terms: 7 + 21n = 9(2 + 5n) + 4 7 + 21n = (2 * 9 + 5n * 9) + 4 7 + 21n = (18 + 45n) + 4 Reorder the terms: 7 + 21n = 18 + 4 + 45n Combine like terms: 18 + 4 = 22 7 + 21n = 22 + 45n Solving 7 + 21n = 22 + 45n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-45n' to each side of the equation. 7 + 21n + -45n = 22 + 45n + -45n Combine like terms: 21n + -45n = -24n 7 + -24n = 22 + 45n + -45n Combine like terms: 45n + -45n = 0 7 + -24n = 22 + 0 7 + -24n = 22 Add '-7' to each side of the equation. 7 + -7 + -24n = 22 + -7 Combine like terms: 7 + -7 = 0 0 + -24n = 22 + -7 -24n = 22 + -7 Combine like terms: 22 + -7 = 15 -24n = 15 Divide each side by '-24'. n = -0.625 Simplifying n = -0.625
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