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Simplifying 45 + -1[4 + -2x + -4(x + 7)] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] Reorder the terms: 45 + -1[4 + -2x + -4(7 + x)] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] 45 + -1[4 + -2x + (7 * -4 + x * -4)] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] 45 + -1[4 + -2x + (-28 + -4x)] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] Reorder the terms: 45 + -1[4 + -28 + -2x + -4x] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] Combine like terms: 4 + -28 = -24 45 + -1[-24 + -2x + -4x] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] Combine like terms: -2x + -4x = -6x 45 + -1[-24 + -6x] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] 45 + [-24 * -1 + -6x * -1] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] 45 + [24 + 6x] = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] Combine like terms: 45 + 24 = 69 69 + 6x = -4(1 + 3x) + -1[4 + -3(x + 2) + -2(2x + -5)] 69 + 6x = (1 * -4 + 3x * -4) + -1[4 + -3(x + 2) + -2(2x + -5)] 69 + 6x = (-4 + -12x) + -1[4 + -3(x + 2) + -2(2x + -5)] Reorder the terms: 69 + 6x = -4 + -12x + -1[4 + -3(2 + x) + -2(2x + -5)] 69 + 6x = -4 + -12x + -1[4 + (2 * -3 + x * -3) + -2(2x + -5)] 69 + 6x = -4 + -12x + -1[4 + (-6 + -3x) + -2(2x + -5)] Reorder the terms: 69 + 6x = -4 + -12x + -1[4 + -6 + -3x + -2(-5 + 2x)] 69 + 6x = -4 + -12x + -1[4 + -6 + -3x + (-5 * -2 + 2x * -2)] 69 + 6x = -4 + -12x + -1[4 + -6 + -3x + (10 + -4x)] Reorder the terms: 69 + 6x = -4 + -12x + -1[4 + -6 + 10 + -3x + -4x] Combine like terms: 4 + -6 = -2 69 + 6x = -4 + -12x + -1[-2 + 10 + -3x + -4x] Combine like terms: -2 + 10 = 8 69 + 6x = -4 + -12x + -1[8 + -3x + -4x] Combine like terms: -3x + -4x = -7x 69 + 6x = -4 + -12x + -1[8 + -7x] 69 + 6x = -4 + -12x + [8 * -1 + -7x * -1] 69 + 6x = -4 + -12x + [-8 + 7x] Reorder the terms: 69 + 6x = -4 + -8 + -12x + 7x Combine like terms: -4 + -8 = -12 69 + 6x = -12 + -12x + 7x Combine like terms: -12x + 7x = -5x 69 + 6x = -12 + -5x Solving 69 + 6x = -12 + -5x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5x' to each side of the equation. 69 + 6x + 5x = -12 + -5x + 5x Combine like terms: 6x + 5x = 11x 69 + 11x = -12 + -5x + 5x Combine like terms: -5x + 5x = 0 69 + 11x = -12 + 0 69 + 11x = -12 Add '-69' to each side of the equation. 69 + -69 + 11x = -12 + -69 Combine like terms: 69 + -69 = 0 0 + 11x = -12 + -69 11x = -12 + -69 Combine like terms: -12 + -69 = -81 11x = -81 Divide each side by '11'. x = -7.363636364 Simplifying x = -7.363636364
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