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Simplifying 10(x + -9) + -9(5 + -6x) = 2(4x + -1) + 5(1 + 2x) Reorder the terms: 10(-9 + x) + -9(5 + -6x) = 2(4x + -1) + 5(1 + 2x) (-9 * 10 + x * 10) + -9(5 + -6x) = 2(4x + -1) + 5(1 + 2x) (-90 + 10x) + -9(5 + -6x) = 2(4x + -1) + 5(1 + 2x) -90 + 10x + (5 * -9 + -6x * -9) = 2(4x + -1) + 5(1 + 2x) -90 + 10x + (-45 + 54x) = 2(4x + -1) + 5(1 + 2x) Reorder the terms: -90 + -45 + 10x + 54x = 2(4x + -1) + 5(1 + 2x) Combine like terms: -90 + -45 = -135 -135 + 10x + 54x = 2(4x + -1) + 5(1 + 2x) Combine like terms: 10x + 54x = 64x -135 + 64x = 2(4x + -1) + 5(1 + 2x) Reorder the terms: -135 + 64x = 2(-1 + 4x) + 5(1 + 2x) -135 + 64x = (-1 * 2 + 4x * 2) + 5(1 + 2x) -135 + 64x = (-2 + 8x) + 5(1 + 2x) -135 + 64x = -2 + 8x + (1 * 5 + 2x * 5) -135 + 64x = -2 + 8x + (5 + 10x) Reorder the terms: -135 + 64x = -2 + 5 + 8x + 10x Combine like terms: -2 + 5 = 3 -135 + 64x = 3 + 8x + 10x Combine like terms: 8x + 10x = 18x -135 + 64x = 3 + 18x Solving -135 + 64x = 3 + 18x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18x' to each side of the equation. -135 + 64x + -18x = 3 + 18x + -18x Combine like terms: 64x + -18x = 46x -135 + 46x = 3 + 18x + -18x Combine like terms: 18x + -18x = 0 -135 + 46x = 3 + 0 -135 + 46x = 3 Add '135' to each side of the equation. -135 + 135 + 46x = 3 + 135 Combine like terms: -135 + 135 = 0 0 + 46x = 3 + 135 46x = 3 + 135 Combine like terms: 3 + 135 = 138 46x = 138 Divide each side by '46'. x = 3 Simplifying x = 3
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