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Simplifying 4(7 + 3x) + -5(6 + -7x) + 1 = 8(1 + 4x) (7 * 4 + 3x * 4) + -5(6 + -7x) + 1 = 8(1 + 4x) (28 + 12x) + -5(6 + -7x) + 1 = 8(1 + 4x) 28 + 12x + (6 * -5 + -7x * -5) + 1 = 8(1 + 4x) 28 + 12x + (-30 + 35x) + 1 = 8(1 + 4x) Reorder the terms: 28 + -30 + 1 + 12x + 35x = 8(1 + 4x) Combine like terms: 28 + -30 = -2 -2 + 1 + 12x + 35x = 8(1 + 4x) Combine like terms: -2 + 1 = -1 -1 + 12x + 35x = 8(1 + 4x) Combine like terms: 12x + 35x = 47x -1 + 47x = 8(1 + 4x) -1 + 47x = (1 * 8 + 4x * 8) -1 + 47x = (8 + 32x) Solving -1 + 47x = 8 + 32x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-32x' to each side of the equation. -1 + 47x + -32x = 8 + 32x + -32x Combine like terms: 47x + -32x = 15x -1 + 15x = 8 + 32x + -32x Combine like terms: 32x + -32x = 0 -1 + 15x = 8 + 0 -1 + 15x = 8 Add '1' to each side of the equation. -1 + 1 + 15x = 8 + 1 Combine like terms: -1 + 1 = 0 0 + 15x = 8 + 1 15x = 8 + 1 Combine like terms: 8 + 1 = 9 15x = 9 Divide each side by '15'. x = 0.6 Simplifying x = 0.6
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