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Simplifying 2[6(x + 3) + -3(x + 5)] + -4x = 6(x + 7) Reorder the terms: 2[6(3 + x) + -3(x + 5)] + -4x = 6(x + 7) 2[(3 * 6 + x * 6) + -3(x + 5)] + -4x = 6(x + 7) 2[(18 + 6x) + -3(x + 5)] + -4x = 6(x + 7) Reorder the terms: 2[18 + 6x + -3(5 + x)] + -4x = 6(x + 7) 2[18 + 6x + (5 * -3 + x * -3)] + -4x = 6(x + 7) 2[18 + 6x + (-15 + -3x)] + -4x = 6(x + 7) Reorder the terms: 2[18 + -15 + 6x + -3x] + -4x = 6(x + 7) Combine like terms: 18 + -15 = 3 2[3 + 6x + -3x] + -4x = 6(x + 7) Combine like terms: 6x + -3x = 3x 2[3 + 3x] + -4x = 6(x + 7) [3 * 2 + 3x * 2] + -4x = 6(x + 7) [6 + 6x] + -4x = 6(x + 7) Combine like terms: 6x + -4x = 2x 6 + 2x = 6(x + 7) Reorder the terms: 6 + 2x = 6(7 + x) 6 + 2x = (7 * 6 + x * 6) 6 + 2x = (42 + 6x) Solving 6 + 2x = 42 + 6x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6x' to each side of the equation. 6 + 2x + -6x = 42 + 6x + -6x Combine like terms: 2x + -6x = -4x 6 + -4x = 42 + 6x + -6x Combine like terms: 6x + -6x = 0 6 + -4x = 42 + 0 6 + -4x = 42 Add '-6' to each side of the equation. 6 + -6 + -4x = 42 + -6 Combine like terms: 6 + -6 = 0 0 + -4x = 42 + -6 -4x = 42 + -6 Combine like terms: 42 + -6 = 36 -4x = 36 Divide each side by '-4'. x = -9 Simplifying x = -9
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