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Simplifying 27x + 113(x + 100) + 52(x + 200) + 19(x + 300) = 106078.14 Reorder the terms: 27x + 113(100 + x) + 52(x + 200) + 19(x + 300) = 106078.14 27x + (100 * 113 + x * 113) + 52(x + 200) + 19(x + 300) = 106078.14 27x + (11300 + 113x) + 52(x + 200) + 19(x + 300) = 106078.14 Reorder the terms: 27x + 11300 + 113x + 52(200 + x) + 19(x + 300) = 106078.14 27x + 11300 + 113x + (200 * 52 + x * 52) + 19(x + 300) = 106078.14 27x + 11300 + 113x + (10400 + 52x) + 19(x + 300) = 106078.14 Reorder the terms: 27x + 11300 + 113x + 10400 + 52x + 19(300 + x) = 106078.14 27x + 11300 + 113x + 10400 + 52x + (300 * 19 + x * 19) = 106078.14 27x + 11300 + 113x + 10400 + 52x + (5700 + 19x) = 106078.14 Reorder the terms: 11300 + 10400 + 5700 + 27x + 113x + 52x + 19x = 106078.14 Combine like terms: 11300 + 10400 = 21700 21700 + 5700 + 27x + 113x + 52x + 19x = 106078.14 Combine like terms: 21700 + 5700 = 27400 27400 + 27x + 113x + 52x + 19x = 106078.14 Combine like terms: 27x + 113x = 140x 27400 + 140x + 52x + 19x = 106078.14 Combine like terms: 140x + 52x = 192x 27400 + 192x + 19x = 106078.14 Combine like terms: 192x + 19x = 211x 27400 + 211x = 106078.14 Solving 27400 + 211x = 106078.14 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27400' to each side of the equation. 27400 + -27400 + 211x = 106078.14 + -27400 Combine like terms: 27400 + -27400 = 0 0 + 211x = 106078.14 + -27400 211x = 106078.14 + -27400 Combine like terms: 106078.14 + -27400 = 78678.14 211x = 78678.14 Divide each side by '211'. x = 372.8821801 Simplifying x = 372.8821801
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