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Simplifying 5(2x + 9) + 2(x + 11) = 3(3x + 4) + 46 Reorder the terms: 5(9 + 2x) + 2(x + 11) = 3(3x + 4) + 46 (9 * 5 + 2x * 5) + 2(x + 11) = 3(3x + 4) + 46 (45 + 10x) + 2(x + 11) = 3(3x + 4) + 46 Reorder the terms: 45 + 10x + 2(11 + x) = 3(3x + 4) + 46 45 + 10x + (11 * 2 + x * 2) = 3(3x + 4) + 46 45 + 10x + (22 + 2x) = 3(3x + 4) + 46 Reorder the terms: 45 + 22 + 10x + 2x = 3(3x + 4) + 46 Combine like terms: 45 + 22 = 67 67 + 10x + 2x = 3(3x + 4) + 46 Combine like terms: 10x + 2x = 12x 67 + 12x = 3(3x + 4) + 46 Reorder the terms: 67 + 12x = 3(4 + 3x) + 46 67 + 12x = (4 * 3 + 3x * 3) + 46 67 + 12x = (12 + 9x) + 46 Reorder the terms: 67 + 12x = 12 + 46 + 9x Combine like terms: 12 + 46 = 58 67 + 12x = 58 + 9x Solving 67 + 12x = 58 + 9x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9x' to each side of the equation. 67 + 12x + -9x = 58 + 9x + -9x Combine like terms: 12x + -9x = 3x 67 + 3x = 58 + 9x + -9x Combine like terms: 9x + -9x = 0 67 + 3x = 58 + 0 67 + 3x = 58 Add '-67' to each side of the equation. 67 + -67 + 3x = 58 + -67 Combine like terms: 67 + -67 = 0 0 + 3x = 58 + -67 3x = 58 + -67 Combine like terms: 58 + -67 = -9 3x = -9 Divide each side by '3'. x = -3 Simplifying x = -3
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