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Simplifying 2(7 + -7(1 + -1n)) + 5n = 22 + 4(6(n + 1) + -3n) 2(7 + (1 * -7 + -1n * -7)) + 5n = 22 + 4(6(n + 1) + -3n) 2(7 + (-7 + 7n)) + 5n = 22 + 4(6(n + 1) + -3n) Combine like terms: 7 + -7 = 0 2(0 + 7n) + 5n = 22 + 4(6(n + 1) + -3n) 2(7n) + 5n = 22 + 4(6(n + 1) + -3n) Remove parenthesis around (7n) 2 * 7n + 5n = 22 + 4(6(n + 1) + -3n) Multiply 2 * 7 14n + 5n = 22 + 4(6(n + 1) + -3n) Combine like terms: 14n + 5n = 19n 19n = 22 + 4(6(n + 1) + -3n) Reorder the terms: 19n = 22 + 4(6(1 + n) + -3n) 19n = 22 + 4((1 * 6 + n * 6) + -3n) 19n = 22 + 4((6 + 6n) + -3n) Combine like terms: 6n + -3n = 3n 19n = 22 + 4(6 + 3n) 19n = 22 + (6 * 4 + 3n * 4) 19n = 22 + (24 + 12n) Combine like terms: 22 + 24 = 46 19n = 46 + 12n Solving 19n = 46 + 12n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-12n' to each side of the equation. 19n + -12n = 46 + 12n + -12n Combine like terms: 19n + -12n = 7n 7n = 46 + 12n + -12n Combine like terms: 12n + -12n = 0 7n = 46 + 0 7n = 46 Divide each side by '7'. n = 6.571428571 Simplifying n = 6.571428571
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