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Simplifying 6(2z + -1) + -2(z + 6) = 7(z + 1) Reorder the terms: 6(-1 + 2z) + -2(z + 6) = 7(z + 1) (-1 * 6 + 2z * 6) + -2(z + 6) = 7(z + 1) (-6 + 12z) + -2(z + 6) = 7(z + 1) Reorder the terms: -6 + 12z + -2(6 + z) = 7(z + 1) -6 + 12z + (6 * -2 + z * -2) = 7(z + 1) -6 + 12z + (-12 + -2z) = 7(z + 1) Reorder the terms: -6 + -12 + 12z + -2z = 7(z + 1) Combine like terms: -6 + -12 = -18 -18 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -18 + 10z = 7(z + 1) Reorder the terms: -18 + 10z = 7(1 + z) -18 + 10z = (1 * 7 + z * 7) -18 + 10z = (7 + 7z) Solving -18 + 10z = 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. -18 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -18 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -18 + 3z = 7 + 0 -18 + 3z = 7 Add '18' to each side of the equation. -18 + 18 + 3z = 7 + 18 Combine like terms: -18 + 18 = 0 0 + 3z = 7 + 18 3z = 7 + 18 Combine like terms: 7 + 18 = 25 3z = 25 Divide each side by '3'. z = 8.333333333 Simplifying z = 8.333333333
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