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Simplifying (3x + 7) + -6 = 12x + -1(x + 4) + -1(4x + 5) Reorder the terms: (7 + 3x) + -6 = 12x + -1(x + 4) + -1(4x + 5) Remove parenthesis around (7 + 3x) 7 + 3x + -6 = 12x + -1(x + 4) + -1(4x + 5) Reorder the terms: 7 + -6 + 3x = 12x + -1(x + 4) + -1(4x + 5) Combine like terms: 7 + -6 = 1 1 + 3x = 12x + -1(x + 4) + -1(4x + 5) Reorder the terms: 1 + 3x = 12x + -1(4 + x) + -1(4x + 5) 1 + 3x = 12x + (4 * -1 + x * -1) + -1(4x + 5) 1 + 3x = 12x + (-4 + -1x) + -1(4x + 5) Reorder the terms: 1 + 3x = 12x + -4 + -1x + -1(5 + 4x) 1 + 3x = 12x + -4 + -1x + (5 * -1 + 4x * -1) 1 + 3x = 12x + -4 + -1x + (-5 + -4x) Reorder the terms: 1 + 3x = -4 + -5 + 12x + -1x + -4x Combine like terms: -4 + -5 = -9 1 + 3x = -9 + 12x + -1x + -4x Combine like terms: 12x + -1x = 11x 1 + 3x = -9 + 11x + -4x Combine like terms: 11x + -4x = 7x 1 + 3x = -9 + 7x Solving 1 + 3x = -9 + 7x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7x' to each side of the equation. 1 + 3x + -7x = -9 + 7x + -7x Combine like terms: 3x + -7x = -4x 1 + -4x = -9 + 7x + -7x Combine like terms: 7x + -7x = 0 1 + -4x = -9 + 0 1 + -4x = -9 Add '-1' to each side of the equation. 1 + -1 + -4x = -9 + -1 Combine like terms: 1 + -1 = 0 0 + -4x = -9 + -1 -4x = -9 + -1 Combine like terms: -9 + -1 = -10 -4x = -10 Divide each side by '-4'. x = 2.5 Simplifying x = 2.5
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