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Simplifying -2(z + 1) + 3(3z + -5) = 6(z + -5) + 8 Reorder the terms: -2(1 + z) + 3(3z + -5) = 6(z + -5) + 8 (1 * -2 + z * -2) + 3(3z + -5) = 6(z + -5) + 8 (-2 + -2z) + 3(3z + -5) = 6(z + -5) + 8 Reorder the terms: -2 + -2z + 3(-5 + 3z) = 6(z + -5) + 8 -2 + -2z + (-5 * 3 + 3z * 3) = 6(z + -5) + 8 -2 + -2z + (-15 + 9z) = 6(z + -5) + 8 Reorder the terms: -2 + -15 + -2z + 9z = 6(z + -5) + 8 Combine like terms: -2 + -15 = -17 -17 + -2z + 9z = 6(z + -5) + 8 Combine like terms: -2z + 9z = 7z -17 + 7z = 6(z + -5) + 8 Reorder the terms: -17 + 7z = 6(-5 + z) + 8 -17 + 7z = (-5 * 6 + z * 6) + 8 -17 + 7z = (-30 + 6z) + 8 Reorder the terms: -17 + 7z = -30 + 8 + 6z Combine like terms: -30 + 8 = -22 -17 + 7z = -22 + 6z Solving -17 + 7z = -22 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -17 + 7z + -6z = -22 + 6z + -6z Combine like terms: 7z + -6z = 1z -17 + 1z = -22 + 6z + -6z Combine like terms: 6z + -6z = 0 -17 + 1z = -22 + 0 -17 + 1z = -22 Add '17' to each side of the equation. -17 + 17 + 1z = -22 + 17 Combine like terms: -17 + 17 = 0 0 + 1z = -22 + 17 1z = -22 + 17 Combine like terms: -22 + 17 = -5 1z = -5 Divide each side by '1'. z = -5 Simplifying z = -5
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