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Simplifying 2[x + -1(3x + 7) + 1] = 2(x + 6) Reorder the terms: 2[x + -1(7 + 3x) + 1] = 2(x + 6) 2[x + (7 * -1 + 3x * -1) + 1] = 2(x + 6) 2[x + (-7 + -3x) + 1] = 2(x + 6) Reorder the terms: 2[-7 + 1 + x + -3x] = 2(x + 6) Combine like terms: -7 + 1 = -6 2[-6 + x + -3x] = 2(x + 6) Combine like terms: x + -3x = -2x 2[-6 + -2x] = 2(x + 6) [-6 * 2 + -2x * 2] = 2(x + 6) [-12 + -4x] = 2(x + 6) Reorder the terms: -12 + -4x = 2(6 + x) -12 + -4x = (6 * 2 + x * 2) -12 + -4x = (12 + 2x) Solving -12 + -4x = 12 + 2x Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2x' to each side of the equation. -12 + -4x + -2x = 12 + 2x + -2x Combine like terms: -4x + -2x = -6x -12 + -6x = 12 + 2x + -2x Combine like terms: 2x + -2x = 0 -12 + -6x = 12 + 0 -12 + -6x = 12 Add '12' to each side of the equation. -12 + 12 + -6x = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -6x = 12 + 12 -6x = 12 + 12 Combine like terms: 12 + 12 = 24 -6x = 24 Divide each side by '-6'. x = -4 Simplifying x = -4
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