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Simplifying 30(50 + -10x) * 26 + -20(50 + 50x) = 30(10x + 1) Reorder the terms for easier multiplication: 30 * 26(50 + -10x) + -20(50 + 50x) = 30(10x + 1) Multiply 30 * 26 780(50 + -10x) + -20(50 + 50x) = 30(10x + 1) (50 * 780 + -10x * 780) + -20(50 + 50x) = 30(10x + 1) (39000 + -7800x) + -20(50 + 50x) = 30(10x + 1) 39000 + -7800x + (50 * -20 + 50x * -20) = 30(10x + 1) 39000 + -7800x + (-1000 + -1000x) = 30(10x + 1) Reorder the terms: 39000 + -1000 + -7800x + -1000x = 30(10x + 1) Combine like terms: 39000 + -1000 = 38000 38000 + -7800x + -1000x = 30(10x + 1) Combine like terms: -7800x + -1000x = -8800x 38000 + -8800x = 30(10x + 1) Reorder the terms: 38000 + -8800x = 30(1 + 10x) 38000 + -8800x = (1 * 30 + 10x * 30) 38000 + -8800x = (30 + 300x) Solving 38000 + -8800x = 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. 38000 + -8800x + -300x = 30 + 300x + -300x Combine like terms: -8800x + -300x = -9100x 38000 + -9100x = 30 + 300x + -300x Combine like terms: 300x + -300x = 0 38000 + -9100x = 30 + 0 38000 + -9100x = 30 Add '-38000' to each side of the equation. 38000 + -38000 + -9100x = 30 + -38000 Combine like terms: 38000 + -38000 = 0 0 + -9100x = 30 + -38000 -9100x = 30 + -38000 Combine like terms: 30 + -38000 = -37970 -9100x = -37970 Divide each side by '-9100'. x = 4.172527473 Simplifying x = 4.172527473
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