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Simplifying -5(6z + -1) + 5(7z + 9) = -1z + 4(z + -7) Reorder the terms: -5(-1 + 6z) + 5(7z + 9) = -1z + 4(z + -7) (-1 * -5 + 6z * -5) + 5(7z + 9) = -1z + 4(z + -7) (5 + -30z) + 5(7z + 9) = -1z + 4(z + -7) Reorder the terms: 5 + -30z + 5(9 + 7z) = -1z + 4(z + -7) 5 + -30z + (9 * 5 + 7z * 5) = -1z + 4(z + -7) 5 + -30z + (45 + 35z) = -1z + 4(z + -7) Reorder the terms: 5 + 45 + -30z + 35z = -1z + 4(z + -7) Combine like terms: 5 + 45 = 50 50 + -30z + 35z = -1z + 4(z + -7) Combine like terms: -30z + 35z = 5z 50 + 5z = -1z + 4(z + -7) Reorder the terms: 50 + 5z = -1z + 4(-7 + z) 50 + 5z = -1z + (-7 * 4 + z * 4) 50 + 5z = -1z + (-28 + 4z) Reorder the terms: 50 + 5z = -28 + -1z + 4z Combine like terms: -1z + 4z = 3z 50 + 5z = -28 + 3z Solving 50 + 5z = -28 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. 50 + 5z + -3z = -28 + 3z + -3z Combine like terms: 5z + -3z = 2z 50 + 2z = -28 + 3z + -3z Combine like terms: 3z + -3z = 0 50 + 2z = -28 + 0 50 + 2z = -28 Add '-50' to each side of the equation. 50 + -50 + 2z = -28 + -50 Combine like terms: 50 + -50 = 0 0 + 2z = -28 + -50 2z = -28 + -50 Combine like terms: -28 + -50 = -78 2z = -78 Divide each side by '2'. z = -39 Simplifying z = -39
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