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Simplifying -2(z + 1) + 3(3z + -7) = 6(z + -6) + 14 Reorder the terms: -2(1 + z) + 3(3z + -7) = 6(z + -6) + 14 (1 * -2 + z * -2) + 3(3z + -7) = 6(z + -6) + 14 (-2 + -2z) + 3(3z + -7) = 6(z + -6) + 14 Reorder the terms: -2 + -2z + 3(-7 + 3z) = 6(z + -6) + 14 -2 + -2z + (-7 * 3 + 3z * 3) = 6(z + -6) + 14 -2 + -2z + (-21 + 9z) = 6(z + -6) + 14 Reorder the terms: -2 + -21 + -2z + 9z = 6(z + -6) + 14 Combine like terms: -2 + -21 = -23 -23 + -2z + 9z = 6(z + -6) + 14 Combine like terms: -2z + 9z = 7z -23 + 7z = 6(z + -6) + 14 Reorder the terms: -23 + 7z = 6(-6 + z) + 14 -23 + 7z = (-6 * 6 + z * 6) + 14 -23 + 7z = (-36 + 6z) + 14 Reorder the terms: -23 + 7z = -36 + 14 + 6z Combine like terms: -36 + 14 = -22 -23 + 7z = -22 + 6z Solving -23 + 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. -23 + 7z + -6z = -22 + 6z + -6z Combine like terms: 7z + -6z = 1z -23 + 1z = -22 + 6z + -6z Combine like terms: 6z + -6z = 0 -23 + 1z = -22 + 0 -23 + 1z = -22 Add '23' to each side of the equation. -23 + 23 + 1z = -22 + 23 Combine like terms: -23 + 23 = 0 0 + 1z = -22 + 23 1z = -22 + 23 Combine like terms: -22 + 23 = 1 1z = 1 Divide each side by '1'. z = 1 Simplifying z = 1
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