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Simplifying -5(1 + -2z) + 4(3 + -1z) + -7(3 + z) = 0 (1 * -5 + -2z * -5) + 4(3 + -1z) + -7(3 + z) = 0 (-5 + 10z) + 4(3 + -1z) + -7(3 + z) = 0 -5 + 10z + (3 * 4 + -1z * 4) + -7(3 + z) = 0 -5 + 10z + (12 + -4z) + -7(3 + z) = 0 -5 + 10z + 12 + -4z + (3 * -7 + z * -7) = 0 -5 + 10z + 12 + -4z + (-21 + -7z) = 0 Reorder the terms: -5 + 12 + -21 + 10z + -4z + -7z = 0 Combine like terms: -5 + 12 = 7 7 + -21 + 10z + -4z + -7z = 0 Combine like terms: 7 + -21 = -14 -14 + 10z + -4z + -7z = 0 Combine like terms: 10z + -4z = 6z -14 + 6z + -7z = 0 Combine like terms: 6z + -7z = -1z -14 + -1z = 0 Solving -14 + -1z = 0 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1z = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1z = 0 + 14 -1z = 0 + 14 Combine like terms: 0 + 14 = 14 -1z = 14 Divide each side by '-1'. z = -14 Simplifying z = -14
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