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Simplifying 6(3 + -1z) + 2(4z + -5) = 2 + -1(3 + -1z) (3 * 6 + -1z * 6) + 2(4z + -5) = 2 + -1(3 + -1z) (18 + -6z) + 2(4z + -5) = 2 + -1(3 + -1z) Reorder the terms: 18 + -6z + 2(-5 + 4z) = 2 + -1(3 + -1z) 18 + -6z + (-5 * 2 + 4z * 2) = 2 + -1(3 + -1z) 18 + -6z + (-10 + 8z) = 2 + -1(3 + -1z) Reorder the terms: 18 + -10 + -6z + 8z = 2 + -1(3 + -1z) Combine like terms: 18 + -10 = 8 8 + -6z + 8z = 2 + -1(3 + -1z) Combine like terms: -6z + 8z = 2z 8 + 2z = 2 + -1(3 + -1z) 8 + 2z = 2 + (3 * -1 + -1z * -1) 8 + 2z = 2 + (-3 + 1z) Combine like terms: 2 + -3 = -1 8 + 2z = -1 + 1z Solving 8 + 2z = -1 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. 8 + 2z + -1z = -1 + 1z + -1z Combine like terms: 2z + -1z = 1z 8 + 1z = -1 + 1z + -1z Combine like terms: 1z + -1z = 0 8 + 1z = -1 + 0 8 + 1z = -1 Add '-8' to each side of the equation. 8 + -8 + 1z = -1 + -8 Combine like terms: 8 + -8 = 0 0 + 1z = -1 + -8 1z = -1 + -8 Combine like terms: -1 + -8 = -9 1z = -9 Divide each side by '1'. z = -9 Simplifying z = -9
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