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Simplifying 100X + 50(1 + -1x) = 200X + -10(1 + -1X) 100X + (1 * 50 + -1x * 50) = 200X + -10(1 + -1X) 100X + (50 + -50x) = 200X + -10(1 + -1X) Reorder the terms: 50 + 100X + -50x = 200X + -10(1 + -1X) 50 + 100X + -50x = 200X + (1 * -10 + -1X * -10) 50 + 100X + -50x = 200X + (-10 + 10X) Reorder the terms: 50 + 100X + -50x = -10 + 200X + 10X Combine like terms: 200X + 10X = 210X 50 + 100X + -50x = -10 + 210X Solving 50 + 100X + -50x = -10 + 210X Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-210X' to each side of the equation. 50 + 100X + -210X + -50x = -10 + 210X + -210X Combine like terms: 100X + -210X = -110X 50 + -110X + -50x = -10 + 210X + -210X Combine like terms: 210X + -210X = 0 50 + -110X + -50x = -10 + 0 50 + -110X + -50x = -10 Add '-50' to each side of the equation. 50 + -110X + -50 + -50x = -10 + -50 Reorder the terms: 50 + -50 + -110X + -50x = -10 + -50 Combine like terms: 50 + -50 = 0 0 + -110X + -50x = -10 + -50 -110X + -50x = -10 + -50 Combine like terms: -10 + -50 = -60 -110X + -50x = -60 Add '50x' to each side of the equation. -110X + -50x + 50x = -60 + 50x Combine like terms: -50x + 50x = 0 -110X + 0 = -60 + 50x -110X = -60 + 50x Divide each side by '-110'. X = 0.5454545455 + -0.4545454545x Simplifying X = 0.5454545455 + -0.4545454545x
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