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Simplifying 2(6z + -1) + -3(z + 4) = 7(z + 1) Reorder the terms: 2(-1 + 6z) + -3(z + 4) = 7(z + 1) (-1 * 2 + 6z * 2) + -3(z + 4) = 7(z + 1) (-2 + 12z) + -3(z + 4) = 7(z + 1) Reorder the terms: -2 + 12z + -3(4 + z) = 7(z + 1) -2 + 12z + (4 * -3 + z * -3) = 7(z + 1) -2 + 12z + (-12 + -3z) = 7(z + 1) Reorder the terms: -2 + -12 + 12z + -3z = 7(z + 1) Combine like terms: -2 + -12 = -14 -14 + 12z + -3z = 7(z + 1) Combine like terms: 12z + -3z = 9z -14 + 9z = 7(z + 1) Reorder the terms: -14 + 9z = 7(1 + z) -14 + 9z = (1 * 7 + z * 7) -14 + 9z = (7 + 7z) Solving -14 + 9z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -14 + 9z + -7z = 7 + 7z + -7z Combine like terms: 9z + -7z = 2z -14 + 2z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -14 + 2z = 7 + 0 -14 + 2z = 7 Add '14' to each side of the equation. -14 + 14 + 2z = 7 + 14 Combine like terms: -14 + 14 = 0 0 + 2z = 7 + 14 2z = 7 + 14 Combine like terms: 7 + 14 = 21 2z = 21 Divide each side by '2'. z = 10.5 Simplifying z = 10.5
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