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Simplifying 2(3x + 4) + 5(3x + 6) = 2(6x + 18) + 4(2x + 4) Reorder the terms: 2(4 + 3x) + 5(3x + 6) = 2(6x + 18) + 4(2x + 4) (4 * 2 + 3x * 2) + 5(3x + 6) = 2(6x + 18) + 4(2x + 4) (8 + 6x) + 5(3x + 6) = 2(6x + 18) + 4(2x + 4) Reorder the terms: 8 + 6x + 5(6 + 3x) = 2(6x + 18) + 4(2x + 4) 8 + 6x + (6 * 5 + 3x * 5) = 2(6x + 18) + 4(2x + 4) 8 + 6x + (30 + 15x) = 2(6x + 18) + 4(2x + 4) Reorder the terms: 8 + 30 + 6x + 15x = 2(6x + 18) + 4(2x + 4) Combine like terms: 8 + 30 = 38 38 + 6x + 15x = 2(6x + 18) + 4(2x + 4) Combine like terms: 6x + 15x = 21x 38 + 21x = 2(6x + 18) + 4(2x + 4) Reorder the terms: 38 + 21x = 2(18 + 6x) + 4(2x + 4) 38 + 21x = (18 * 2 + 6x * 2) + 4(2x + 4) 38 + 21x = (36 + 12x) + 4(2x + 4) Reorder the terms: 38 + 21x = 36 + 12x + 4(4 + 2x) 38 + 21x = 36 + 12x + (4 * 4 + 2x * 4) 38 + 21x = 36 + 12x + (16 + 8x) Reorder the terms: 38 + 21x = 36 + 16 + 12x + 8x Combine like terms: 36 + 16 = 52 38 + 21x = 52 + 12x + 8x Combine like terms: 12x + 8x = 20x 38 + 21x = 52 + 20x Solving 38 + 21x = 52 + 20x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20x' to each side of the equation. 38 + 21x + -20x = 52 + 20x + -20x Combine like terms: 21x + -20x = 1x 38 + 1x = 52 + 20x + -20x Combine like terms: 20x + -20x = 0 38 + 1x = 52 + 0 38 + 1x = 52 Add '-38' to each side of the equation. 38 + -38 + 1x = 52 + -38 Combine like terms: 38 + -38 = 0 0 + 1x = 52 + -38 1x = 52 + -38 Combine like terms: 52 + -38 = 14 1x = 14 Divide each side by '1'. x = 14 Simplifying x = 14
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