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Simplifying 2(x + -1y + -1z) + 3(x + 4) = 0 (x * 2 + -1y * 2 + -1z * 2) + 3(x + 4) = 0 (2x + -2y + -2z) + 3(x + 4) = 0 Reorder the terms: 2x + -2y + -2z + 3(4 + x) = 0 2x + -2y + -2z + (4 * 3 + x * 3) = 0 2x + -2y + -2z + (12 + 3x) = 0 Reorder the terms: 12 + 2x + 3x + -2y + -2z = 0 Combine like terms: 2x + 3x = 5x 12 + 5x + -2y + -2z = 0 Solving 12 + 5x + -2y + -2z = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + 5x + -2y + -12 + -2z = 0 + -12 Reorder the terms: 12 + -12 + 5x + -2y + -2z = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 5x + -2y + -2z = 0 + -12 5x + -2y + -2z = 0 + -12 Combine like terms: 0 + -12 = -12 5x + -2y + -2z = -12 Add '2y' to each side of the equation. 5x + -2y + 2y + -2z = -12 + 2y Combine like terms: -2y + 2y = 0 5x + 0 + -2z = -12 + 2y 5x + -2z = -12 + 2y Add '2z' to each side of the equation. 5x + -2z + 2z = -12 + 2y + 2z Combine like terms: -2z + 2z = 0 5x + 0 = -12 + 2y + 2z 5x = -12 + 2y + 2z Divide each side by '5'. x = -2.4 + 0.4y + 0.4z Simplifying x = -2.4 + 0.4y + 0.4z
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