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Simplifying 5z + 4(5 + -1z) = -1(z + -5) + 7 5z + (5 * 4 + -1z * 4) = -1(z + -5) + 7 5z + (20 + -4z) = -1(z + -5) + 7 Reorder the terms: 20 + 5z + -4z = -1(z + -5) + 7 Combine like terms: 5z + -4z = 1z 20 + 1z = -1(z + -5) + 7 Reorder the terms: 20 + 1z = -1(-5 + z) + 7 20 + 1z = (-5 * -1 + z * -1) + 7 20 + 1z = (5 + -1z) + 7 Reorder the terms: 20 + 1z = 5 + 7 + -1z Combine like terms: 5 + 7 = 12 20 + 1z = 12 + -1z Solving 20 + 1z = 12 + -1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add 'z' to each side of the equation. 20 + 1z + z = 12 + -1z + z Combine like terms: 1z + z = 2z 20 + 2z = 12 + -1z + z Combine like terms: -1z + z = 0 20 + 2z = 12 + 0 20 + 2z = 12 Add '-20' to each side of the equation. 20 + -20 + 2z = 12 + -20 Combine like terms: 20 + -20 = 0 0 + 2z = 12 + -20 2z = 12 + -20 Combine like terms: 12 + -20 = -8 2z = -8 Divide each side by '2'. z = -4 Simplifying z = -4
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