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Simplifying (3x + -5y + 2z + -6) + -1(2x + 5y + 6z + -7) = 0 Reorder the terms: (-6 + 3x + -5y + 2z) + -1(2x + 5y + 6z + -7) = 0 Remove parenthesis around (-6 + 3x + -5y + 2z) -6 + 3x + -5y + 2z + -1(2x + 5y + 6z + -7) = 0 Reorder the terms: -6 + 3x + -5y + 2z + -1(-7 + 2x + 5y + 6z) = 0 -6 + 3x + -5y + 2z + (-7 * -1 + 2x * -1 + 5y * -1 + 6z * -1) = 0 -6 + 3x + -5y + 2z + (7 + -2x + -5y + -6z) = 0 Reorder the terms: -6 + 7 + 3x + -2x + -5y + -5y + 2z + -6z = 0 Combine like terms: -6 + 7 = 1 1 + 3x + -2x + -5y + -5y + 2z + -6z = 0 Combine like terms: 3x + -2x = 1x 1 + 1x + -5y + -5y + 2z + -6z = 0 Combine like terms: -5y + -5y = -10y 1 + 1x + -10y + 2z + -6z = 0 Combine like terms: 2z + -6z = -4z 1 + 1x + -10y + -4z = 0 Solving 1 + 1x + -10y + -4z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 1x + -10y + -1 + -4z = 0 + -1 Reorder the terms: 1 + -1 + 1x + -10y + -4z = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1x + -10y + -4z = 0 + -1 1x + -10y + -4z = 0 + -1 Combine like terms: 0 + -1 = -1 1x + -10y + -4z = -1 Add '10y' to each side of the equation. 1x + -10y + 10y + -4z = -1 + 10y Combine like terms: -10y + 10y = 0 1x + 0 + -4z = -1 + 10y 1x + -4z = -1 + 10y Add '4z' to each side of the equation. 1x + -4z + 4z = -1 + 10y + 4z Combine like terms: -4z + 4z = 0 1x + 0 = -1 + 10y + 4z 1x = -1 + 10y + 4z Divide each side by '1'. x = -1 + 10y + 4z Simplifying x = -1 + 10y + 4z
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