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Simplifying -4z + 27 + -4(z + -2) = 6z + -1(2z + -1) + -5z + 6 Reorder the terms: -4z + 27 + -4(-2 + z) = 6z + -1(2z + -1) + -5z + 6 -4z + 27 + (-2 * -4 + z * -4) = 6z + -1(2z + -1) + -5z + 6 -4z + 27 + (8 + -4z) = 6z + -1(2z + -1) + -5z + 6 Reorder the terms: 27 + 8 + -4z + -4z = 6z + -1(2z + -1) + -5z + 6 Combine like terms: 27 + 8 = 35 35 + -4z + -4z = 6z + -1(2z + -1) + -5z + 6 Combine like terms: -4z + -4z = -8z 35 + -8z = 6z + -1(2z + -1) + -5z + 6 Reorder the terms: 35 + -8z = 6z + -1(-1 + 2z) + -5z + 6 35 + -8z = 6z + (-1 * -1 + 2z * -1) + -5z + 6 35 + -8z = 6z + (1 + -2z) + -5z + 6 Reorder the terms: 35 + -8z = 1 + 6 + 6z + -2z + -5z Combine like terms: 1 + 6 = 7 35 + -8z = 7 + 6z + -2z + -5z Combine like terms: 6z + -2z = 4z 35 + -8z = 7 + 4z + -5z Combine like terms: 4z + -5z = -1z 35 + -8z = 7 + -1z Solving 35 + -8z = 7 + -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. 35 + -8z + z = 7 + -1z + z Combine like terms: -8z + z = -7z 35 + -7z = 7 + -1z + z Combine like terms: -1z + z = 0 35 + -7z = 7 + 0 35 + -7z = 7 Add '-35' to each side of the equation. 35 + -35 + -7z = 7 + -35 Combine like terms: 35 + -35 = 0 0 + -7z = 7 + -35 -7z = 7 + -35 Combine like terms: 7 + -35 = -28 -7z = -28 Divide each side by '-7'. z = 4 Simplifying z = 4
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