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Simplifying 2(3x + -7) + 4(3x + 2) = 6(5x + 9) + 12 Reorder the terms: 2(-7 + 3x) + 4(3x + 2) = 6(5x + 9) + 12 (-7 * 2 + 3x * 2) + 4(3x + 2) = 6(5x + 9) + 12 (-14 + 6x) + 4(3x + 2) = 6(5x + 9) + 12 Reorder the terms: -14 + 6x + 4(2 + 3x) = 6(5x + 9) + 12 -14 + 6x + (2 * 4 + 3x * 4) = 6(5x + 9) + 12 -14 + 6x + (8 + 12x) = 6(5x + 9) + 12 Reorder the terms: -14 + 8 + 6x + 12x = 6(5x + 9) + 12 Combine like terms: -14 + 8 = -6 -6 + 6x + 12x = 6(5x + 9) + 12 Combine like terms: 6x + 12x = 18x -6 + 18x = 6(5x + 9) + 12 Reorder the terms: -6 + 18x = 6(9 + 5x) + 12 -6 + 18x = (9 * 6 + 5x * 6) + 12 -6 + 18x = (54 + 30x) + 12 Reorder the terms: -6 + 18x = 54 + 12 + 30x Combine like terms: 54 + 12 = 66 -6 + 18x = 66 + 30x Solving -6 + 18x = 66 + 30x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30x' to each side of the equation. -6 + 18x + -30x = 66 + 30x + -30x Combine like terms: 18x + -30x = -12x -6 + -12x = 66 + 30x + -30x Combine like terms: 30x + -30x = 0 -6 + -12x = 66 + 0 -6 + -12x = 66 Add '6' to each side of the equation. -6 + 6 + -12x = 66 + 6 Combine like terms: -6 + 6 = 0 0 + -12x = 66 + 6 -12x = 66 + 6 Combine like terms: 66 + 6 = 72 -12x = 72 Divide each side by '-12'. x = -6 Simplifying x = -6
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