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Simplifying 78 + -3(2x + -1) + 4(2 + -1x) = 2(x + -5) + -3(2 + -3x) Reorder the terms: 78 + -3(-1 + 2x) + 4(2 + -1x) = 2(x + -5) + -3(2 + -3x) 78 + (-1 * -3 + 2x * -3) + 4(2 + -1x) = 2(x + -5) + -3(2 + -3x) 78 + (3 + -6x) + 4(2 + -1x) = 2(x + -5) + -3(2 + -3x) 78 + 3 + -6x + (2 * 4 + -1x * 4) = 2(x + -5) + -3(2 + -3x) 78 + 3 + -6x + (8 + -4x) = 2(x + -5) + -3(2 + -3x) Reorder the terms: 78 + 3 + 8 + -6x + -4x = 2(x + -5) + -3(2 + -3x) Combine like terms: 78 + 3 = 81 81 + 8 + -6x + -4x = 2(x + -5) + -3(2 + -3x) Combine like terms: 81 + 8 = 89 89 + -6x + -4x = 2(x + -5) + -3(2 + -3x) Combine like terms: -6x + -4x = -10x 89 + -10x = 2(x + -5) + -3(2 + -3x) Reorder the terms: 89 + -10x = 2(-5 + x) + -3(2 + -3x) 89 + -10x = (-5 * 2 + x * 2) + -3(2 + -3x) 89 + -10x = (-10 + 2x) + -3(2 + -3x) 89 + -10x = -10 + 2x + (2 * -3 + -3x * -3) 89 + -10x = -10 + 2x + (-6 + 9x) Reorder the terms: 89 + -10x = -10 + -6 + 2x + 9x Combine like terms: -10 + -6 = -16 89 + -10x = -16 + 2x + 9x Combine like terms: 2x + 9x = 11x 89 + -10x = -16 + 11x Solving 89 + -10x = -16 + 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. 89 + -10x + -11x = -16 + 11x + -11x Combine like terms: -10x + -11x = -21x 89 + -21x = -16 + 11x + -11x Combine like terms: 11x + -11x = 0 89 + -21x = -16 + 0 89 + -21x = -16 Add '-89' to each side of the equation. 89 + -89 + -21x = -16 + -89 Combine like terms: 89 + -89 = 0 0 + -21x = -16 + -89 -21x = -16 + -89 Combine like terms: -16 + -89 = -105 -21x = -105 Divide each side by '-21'. x = 5 Simplifying x = 5
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