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Simplifying 45(x + -1) + -40(3x + 1) = 12(x + 1) Reorder the terms: 45(-1 + x) + -40(3x + 1) = 12(x + 1) (-1 * 45 + x * 45) + -40(3x + 1) = 12(x + 1) (-45 + 45x) + -40(3x + 1) = 12(x + 1) Reorder the terms: -45 + 45x + -40(1 + 3x) = 12(x + 1) -45 + 45x + (1 * -40 + 3x * -40) = 12(x + 1) -45 + 45x + (-40 + -120x) = 12(x + 1) Reorder the terms: -45 + -40 + 45x + -120x = 12(x + 1) Combine like terms: -45 + -40 = -85 -85 + 45x + -120x = 12(x + 1) Combine like terms: 45x + -120x = -75x -85 + -75x = 12(x + 1) Reorder the terms: -85 + -75x = 12(1 + x) -85 + -75x = (1 * 12 + x * 12) -85 + -75x = (12 + 12x) Solving -85 + -75x = 12 + 12x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12x' to each side of the equation. -85 + -75x + -12x = 12 + 12x + -12x Combine like terms: -75x + -12x = -87x -85 + -87x = 12 + 12x + -12x Combine like terms: 12x + -12x = 0 -85 + -87x = 12 + 0 -85 + -87x = 12 Add '85' to each side of the equation. -85 + 85 + -87x = 12 + 85 Combine like terms: -85 + 85 = 0 0 + -87x = 12 + 85 -87x = 12 + 85 Combine like terms: 12 + 85 = 97 -87x = 97 Divide each side by '-87'. x = -1.114942529 Simplifying x = -1.114942529
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