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Simplifying 30(50 + -10x) + -20(50 + 50 + 50x) = 30(10x + 1) (50 * 30 + -10x * 30) + -20(50 + 50 + 50x) = 30(10x + 1) (1500 + -300x) + -20(50 + 50 + 50x) = 30(10x + 1) Combine like terms: 50 + 50 = 100 1500 + -300x + -20(100 + 50x) = 30(10x + 1) 1500 + -300x + (100 * -20 + 50x * -20) = 30(10x + 1) 1500 + -300x + (-2000 + -1000x) = 30(10x + 1) Reorder the terms: 1500 + -2000 + -300x + -1000x = 30(10x + 1) Combine like terms: 1500 + -2000 = -500 -500 + -300x + -1000x = 30(10x + 1) Combine like terms: -300x + -1000x = -1300x -500 + -1300x = 30(10x + 1) Reorder the terms: -500 + -1300x = 30(1 + 10x) -500 + -1300x = (1 * 30 + 10x * 30) -500 + -1300x = (30 + 300x) Solving -500 + -1300x = 30 + 300x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300x' to each side of the equation. -500 + -1300x + -300x = 30 + 300x + -300x Combine like terms: -1300x + -300x = -1600x -500 + -1600x = 30 + 300x + -300x Combine like terms: 300x + -300x = 0 -500 + -1600x = 30 + 0 -500 + -1600x = 30 Add '500' to each side of the equation. -500 + 500 + -1600x = 30 + 500 Combine like terms: -500 + 500 = 0 0 + -1600x = 30 + 500 -1600x = 30 + 500 Combine like terms: 30 + 500 = 530 -1600x = 530 Divide each side by '-1600'. x = -0.33125 Simplifying x = -0.33125
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