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Simplifying 5(6x + 2) + 7(4 + -12x) = 35 + -1(6 + 27x) Reorder the terms: 5(2 + 6x) + 7(4 + -12x) = 35 + -1(6 + 27x) (2 * 5 + 6x * 5) + 7(4 + -12x) = 35 + -1(6 + 27x) (10 + 30x) + 7(4 + -12x) = 35 + -1(6 + 27x) 10 + 30x + (4 * 7 + -12x * 7) = 35 + -1(6 + 27x) 10 + 30x + (28 + -84x) = 35 + -1(6 + 27x) Reorder the terms: 10 + 28 + 30x + -84x = 35 + -1(6 + 27x) Combine like terms: 10 + 28 = 38 38 + 30x + -84x = 35 + -1(6 + 27x) Combine like terms: 30x + -84x = -54x 38 + -54x = 35 + -1(6 + 27x) 38 + -54x = 35 + (6 * -1 + 27x * -1) 38 + -54x = 35 + (-6 + -27x) Combine like terms: 35 + -6 = 29 38 + -54x = 29 + -27x Solving 38 + -54x = 29 + -27x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27x' to each side of the equation. 38 + -54x + 27x = 29 + -27x + 27x Combine like terms: -54x + 27x = -27x 38 + -27x = 29 + -27x + 27x Combine like terms: -27x + 27x = 0 38 + -27x = 29 + 0 38 + -27x = 29 Add '-38' to each side of the equation. 38 + -38 + -27x = 29 + -38 Combine like terms: 38 + -38 = 0 0 + -27x = 29 + -38 -27x = 29 + -38 Combine like terms: 29 + -38 = -9 -27x = -9 Divide each side by '-27'. x = 0.3333333333 Simplifying x = 0.3333333333
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