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Simplifying 3z + -1z + 4(1 + -1z) = 5(1 + -2z) + -12 3z + -1z + (1 * 4 + -1z * 4) = 5(1 + -2z) + -12 3z + -1z + (4 + -4z) = 5(1 + -2z) + -12 Reorder the terms: 4 + 3z + -1z + -4z = 5(1 + -2z) + -12 Combine like terms: 3z + -1z = 2z 4 + 2z + -4z = 5(1 + -2z) + -12 Combine like terms: 2z + -4z = -2z 4 + -2z = 5(1 + -2z) + -12 4 + -2z = (1 * 5 + -2z * 5) + -12 4 + -2z = (5 + -10z) + -12 Reorder the terms: 4 + -2z = 5 + -12 + -10z Combine like terms: 5 + -12 = -7 4 + -2z = -7 + -10z Solving 4 + -2z = -7 + -10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10z' to each side of the equation. 4 + -2z + 10z = -7 + -10z + 10z Combine like terms: -2z + 10z = 8z 4 + 8z = -7 + -10z + 10z Combine like terms: -10z + 10z = 0 4 + 8z = -7 + 0 4 + 8z = -7 Add '-4' to each side of the equation. 4 + -4 + 8z = -7 + -4 Combine like terms: 4 + -4 = 0 0 + 8z = -7 + -4 8z = -7 + -4 Combine like terms: -7 + -4 = -11 8z = -11 Divide each side by '8'. z = -1.375 Simplifying z = -1.375
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