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Simplifying 6(-5x + 1) + -3(4x + -12) = 3x + -9 + -1(3x + -9) Reorder the terms: 6(1 + -5x) + -3(4x + -12) = 3x + -9 + -1(3x + -9) (1 * 6 + -5x * 6) + -3(4x + -12) = 3x + -9 + -1(3x + -9) (6 + -30x) + -3(4x + -12) = 3x + -9 + -1(3x + -9) Reorder the terms: 6 + -30x + -3(-12 + 4x) = 3x + -9 + -1(3x + -9) 6 + -30x + (-12 * -3 + 4x * -3) = 3x + -9 + -1(3x + -9) 6 + -30x + (36 + -12x) = 3x + -9 + -1(3x + -9) Reorder the terms: 6 + 36 + -30x + -12x = 3x + -9 + -1(3x + -9) Combine like terms: 6 + 36 = 42 42 + -30x + -12x = 3x + -9 + -1(3x + -9) Combine like terms: -30x + -12x = -42x 42 + -42x = 3x + -9 + -1(3x + -9) Reorder the terms: 42 + -42x = 3x + -9 + -1(-9 + 3x) 42 + -42x = 3x + -9 + (-9 * -1 + 3x * -1) 42 + -42x = 3x + -9 + (9 + -3x) Reorder the terms: 42 + -42x = -9 + 9 + 3x + -3x Combine like terms: -9 + 9 = 0 42 + -42x = 0 + 3x + -3x 42 + -42x = 3x + -3x Combine like terms: 3x + -3x = 0 42 + -42x = 0 Solving 42 + -42x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + -42x = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -42x = 0 + -42 -42x = 0 + -42 Combine like terms: 0 + -42 = -42 -42x = -42 Divide each side by '-42'. x = 1 Simplifying x = 1
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