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