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Simplifying 12(x + 1) + -1(42 + -3x) = 42(x + -1) Reorder the terms: 12(1 + x) + -1(42 + -3x) = 42(x + -1) (1 * 12 + x * 12) + -1(42 + -3x) = 42(x + -1) (12 + 12x) + -1(42 + -3x) = 42(x + -1) 12 + 12x + (42 * -1 + -3x * -1) = 42(x + -1) 12 + 12x + (-42 + 3x) = 42(x + -1) Reorder the terms: 12 + -42 + 12x + 3x = 42(x + -1) Combine like terms: 12 + -42 = -30 -30 + 12x + 3x = 42(x + -1) Combine like terms: 12x + 3x = 15x -30 + 15x = 42(x + -1) Reorder the terms: -30 + 15x = 42(-1 + x) -30 + 15x = (-1 * 42 + x * 42) -30 + 15x = (-42 + 42x) Solving -30 + 15x = -42 + 42x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42x' to each side of the equation. -30 + 15x + -42x = -42 + 42x + -42x Combine like terms: 15x + -42x = -27x -30 + -27x = -42 + 42x + -42x Combine like terms: 42x + -42x = 0 -30 + -27x = -42 + 0 -30 + -27x = -42 Add '30' to each side of the equation. -30 + 30 + -27x = -42 + 30 Combine like terms: -30 + 30 = 0 0 + -27x = -42 + 30 -27x = -42 + 30 Combine like terms: -42 + 30 = -12 -27x = -12 Divide each side by '-27'. x = 0.4444444444 Simplifying x = 0.4444444444
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