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Simplifying 8(2x + 3) + -1[12 + -1(24x + -18)] = 2(6x + 4) + [21x + -1(6x + -25)] Reorder the terms: 8(3 + 2x) + -1[12 + -1(24x + -18)] = 2(6x + 4) + [21x + -1(6x + -25)] (3 * 8 + 2x * 8) + -1[12 + -1(24x + -18)] = 2(6x + 4) + [21x + -1(6x + -25)] (24 + 16x) + -1[12 + -1(24x + -18)] = 2(6x + 4) + [21x + -1(6x + -25)] Reorder the terms: 24 + 16x + -1[12 + -1(-18 + 24x)] = 2(6x + 4) + [21x + -1(6x + -25)] 24 + 16x + -1[12 + (-18 * -1 + 24x * -1)] = 2(6x + 4) + [21x + -1(6x + -25)] 24 + 16x + -1[12 + (18 + -24x)] = 2(6x + 4) + [21x + -1(6x + -25)] Combine like terms: 12 + 18 = 30 24 + 16x + -1[30 + -24x] = 2(6x + 4) + [21x + -1(6x + -25)] 24 + 16x + [30 * -1 + -24x * -1] = 2(6x + 4) + [21x + -1(6x + -25)] 24 + 16x + [-30 + 24x] = 2(6x + 4) + [21x + -1(6x + -25)] Reorder the terms: 24 + -30 + 16x + 24x = 2(6x + 4) + [21x + -1(6x + -25)] Combine like terms: 24 + -30 = -6 -6 + 16x + 24x = 2(6x + 4) + [21x + -1(6x + -25)] Combine like terms: 16x + 24x = 40x -6 + 40x = 2(6x + 4) + [21x + -1(6x + -25)] Reorder the terms: -6 + 40x = 2(4 + 6x) + [21x + -1(6x + -25)] -6 + 40x = (4 * 2 + 6x * 2) + [21x + -1(6x + -25)] -6 + 40x = (8 + 12x) + [21x + -1(6x + -25)] Reorder the terms: -6 + 40x = 8 + 12x + [21x + -1(-25 + 6x)] -6 + 40x = 8 + 12x + [21x + (-25 * -1 + 6x * -1)] -6 + 40x = 8 + 12x + [21x + (25 + -6x)] Reorder the terms: -6 + 40x = 8 + 12x + [25 + 21x + -6x] Combine like terms: 21x + -6x = 15x -6 + 40x = 8 + 12x + [25 + 15x] Remove brackets around [25 + 15x] -6 + 40x = 8 + 12x + 25 + 15x Reorder the terms: -6 + 40x = 8 + 25 + 12x + 15x Combine like terms: 8 + 25 = 33 -6 + 40x = 33 + 12x + 15x Combine like terms: 12x + 15x = 27x -6 + 40x = 33 + 27x Solving -6 + 40x = 33 + 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. -6 + 40x + -27x = 33 + 27x + -27x Combine like terms: 40x + -27x = 13x -6 + 13x = 33 + 27x + -27x Combine like terms: 27x + -27x = 0 -6 + 13x = 33 + 0 -6 + 13x = 33 Add '6' to each side of the equation. -6 + 6 + 13x = 33 + 6 Combine like terms: -6 + 6 = 0 0 + 13x = 33 + 6 13x = 33 + 6 Combine like terms: 33 + 6 = 39 13x = 39 Divide each side by '13'. x = 3 Simplifying x = 3
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