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Simplifying 34 + -52(12n + -34) + 235 = 32 + 101(35n + -1) Reorder the terms: 34 + -52(-34 + 12n) + 235 = 32 + 101(35n + -1) 34 + (-34 * -52 + 12n * -52) + 235 = 32 + 101(35n + -1) 34 + (1768 + -624n) + 235 = 32 + 101(35n + -1) Reorder the terms: 34 + 1768 + 235 + -624n = 32 + 101(35n + -1) Combine like terms: 34 + 1768 = 1802 1802 + 235 + -624n = 32 + 101(35n + -1) Combine like terms: 1802 + 235 = 2037 2037 + -624n = 32 + 101(35n + -1) Reorder the terms: 2037 + -624n = 32 + 101(-1 + 35n) 2037 + -624n = 32 + (-1 * 101 + 35n * 101) 2037 + -624n = 32 + (-101 + 3535n) Combine like terms: 32 + -101 = -69 2037 + -624n = -69 + 3535n Solving 2037 + -624n = -69 + 3535n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3535n' to each side of the equation. 2037 + -624n + -3535n = -69 + 3535n + -3535n Combine like terms: -624n + -3535n = -4159n 2037 + -4159n = -69 + 3535n + -3535n Combine like terms: 3535n + -3535n = 0 2037 + -4159n = -69 + 0 2037 + -4159n = -69 Add '-2037' to each side of the equation. 2037 + -2037 + -4159n = -69 + -2037 Combine like terms: 2037 + -2037 = 0 0 + -4159n = -69 + -2037 -4159n = -69 + -2037 Combine like terms: -69 + -2037 = -2106 -4159n = -2106 Divide each side by '-4159'. n = 0.506371724 Simplifying n = 0.506371724
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