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Simplifying 12(3x + 4) + -6(2x + -5) = 4x + -42 Reorder the terms: 12(4 + 3x) + -6(2x + -5) = 4x + -42 (4 * 12 + 3x * 12) + -6(2x + -5) = 4x + -42 (48 + 36x) + -6(2x + -5) = 4x + -42 Reorder the terms: 48 + 36x + -6(-5 + 2x) = 4x + -42 48 + 36x + (-5 * -6 + 2x * -6) = 4x + -42 48 + 36x + (30 + -12x) = 4x + -42 Reorder the terms: 48 + 30 + 36x + -12x = 4x + -42 Combine like terms: 48 + 30 = 78 78 + 36x + -12x = 4x + -42 Combine like terms: 36x + -12x = 24x 78 + 24x = 4x + -42 Reorder the terms: 78 + 24x = -42 + 4x Solving 78 + 24x = -42 + 4x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4x' to each side of the equation. 78 + 24x + -4x = -42 + 4x + -4x Combine like terms: 24x + -4x = 20x 78 + 20x = -42 + 4x + -4x Combine like terms: 4x + -4x = 0 78 + 20x = -42 + 0 78 + 20x = -42 Add '-78' to each side of the equation. 78 + -78 + 20x = -42 + -78 Combine like terms: 78 + -78 = 0 0 + 20x = -42 + -78 20x = -42 + -78 Combine like terms: -42 + -78 = -120 20x = -120 Divide each side by '20'. x = -6 Simplifying x = -6
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