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Simplifying 3(2x + -2) + 3(x + 6) = 7(x + 7) + -1(x + 6) Reorder the terms: 3(-2 + 2x) + 3(x + 6) = 7(x + 7) + -1(x + 6) (-2 * 3 + 2x * 3) + 3(x + 6) = 7(x + 7) + -1(x + 6) (-6 + 6x) + 3(x + 6) = 7(x + 7) + -1(x + 6) Reorder the terms: -6 + 6x + 3(6 + x) = 7(x + 7) + -1(x + 6) -6 + 6x + (6 * 3 + x * 3) = 7(x + 7) + -1(x + 6) -6 + 6x + (18 + 3x) = 7(x + 7) + -1(x + 6) Reorder the terms: -6 + 18 + 6x + 3x = 7(x + 7) + -1(x + 6) Combine like terms: -6 + 18 = 12 12 + 6x + 3x = 7(x + 7) + -1(x + 6) Combine like terms: 6x + 3x = 9x 12 + 9x = 7(x + 7) + -1(x + 6) Reorder the terms: 12 + 9x = 7(7 + x) + -1(x + 6) 12 + 9x = (7 * 7 + x * 7) + -1(x + 6) 12 + 9x = (49 + 7x) + -1(x + 6) Reorder the terms: 12 + 9x = 49 + 7x + -1(6 + x) 12 + 9x = 49 + 7x + (6 * -1 + x * -1) 12 + 9x = 49 + 7x + (-6 + -1x) Reorder the terms: 12 + 9x = 49 + -6 + 7x + -1x Combine like terms: 49 + -6 = 43 12 + 9x = 43 + 7x + -1x Combine like terms: 7x + -1x = 6x 12 + 9x = 43 + 6x Solving 12 + 9x = 43 + 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. 12 + 9x + -6x = 43 + 6x + -6x Combine like terms: 9x + -6x = 3x 12 + 3x = 43 + 6x + -6x Combine like terms: 6x + -6x = 0 12 + 3x = 43 + 0 12 + 3x = 43 Add '-12' to each side of the equation. 12 + -12 + 3x = 43 + -12 Combine like terms: 12 + -12 = 0 0 + 3x = 43 + -12 3x = 43 + -12 Combine like terms: 43 + -12 = 31 3x = 31 Divide each side by '3'. x = 10.33333333 Simplifying x = 10.33333333
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