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Simplifying 6(3x + 4) + -2(x + 9) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 Reorder the terms: 6(4 + 3x) + -2(x + 9) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 (4 * 6 + 3x * 6) + -2(x + 9) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 (24 + 18x) + -2(x + 9) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 Reorder the terms: 24 + 18x + -2(9 + x) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 24 + 18x + (9 * -2 + x * -2) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 24 + 18x + (-18 + -2x) + -10(y + -5x) + 5(9x + 2y + -4) = 11(x + 13) + 43 Reorder the terms: 24 + 18x + -18 + -2x + -10(-5x + y) + 5(9x + 2y + -4) = 11(x + 13) + 43 24 + 18x + -18 + -2x + (-5x * -10 + y * -10) + 5(9x + 2y + -4) = 11(x + 13) + 43 24 + 18x + -18 + -2x + (50x + -10y) + 5(9x + 2y + -4) = 11(x + 13) + 43 Reorder the terms: 24 + 18x + -18 + -2x + 50x + -10y + 5(-4 + 9x + 2y) = 11(x + 13) + 43 24 + 18x + -18 + -2x + 50x + -10y + (-4 * 5 + 9x * 5 + 2y * 5) = 11(x + 13) + 43 24 + 18x + -18 + -2x + 50x + -10y + (-20 + 45x + 10y) = 11(x + 13) + 43 Reorder the terms: 24 + -18 + -20 + 18x + -2x + 50x + 45x + -10y + 10y = 11(x + 13) + 43 Combine like terms: 24 + -18 = 6 6 + -20 + 18x + -2x + 50x + 45x + -10y + 10y = 11(x + 13) + 43 Combine like terms: 6 + -20 = -14 -14 + 18x + -2x + 50x + 45x + -10y + 10y = 11(x + 13) + 43 Combine like terms: 18x + -2x = 16x -14 + 16x + 50x + 45x + -10y + 10y = 11(x + 13) + 43 Combine like terms: 16x + 50x = 66x -14 + 66x + 45x + -10y + 10y = 11(x + 13) + 43 Combine like terms: 66x + 45x = 111x -14 + 111x + -10y + 10y = 11(x + 13) + 43 Combine like terms: -10y + 10y = 0 -14 + 111x + 0 = 11(x + 13) + 43 -14 + 111x = 11(x + 13) + 43 Reorder the terms: -14 + 111x = 11(13 + x) + 43 -14 + 111x = (13 * 11 + x * 11) + 43 -14 + 111x = (143 + 11x) + 43 Reorder the terms: -14 + 111x = 143 + 43 + 11x Combine like terms: 143 + 43 = 186 -14 + 111x = 186 + 11x Solving -14 + 111x = 186 + 11x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-11x' to each side of the equation. -14 + 111x + -11x = 186 + 11x + -11x Combine like terms: 111x + -11x = 100x -14 + 100x = 186 + 11x + -11x Combine like terms: 11x + -11x = 0 -14 + 100x = 186 + 0 -14 + 100x = 186 Add '14' to each side of the equation. -14 + 14 + 100x = 186 + 14 Combine like terms: -14 + 14 = 0 0 + 100x = 186 + 14 100x = 186 + 14 Combine like terms: 186 + 14 = 200 100x = 200 Divide each side by '100'. x = 2 Simplifying x = 2
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