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Simplifying 6(2z + -1) + -2(z + 9) = 7(z + 1) Reorder the terms: 6(-1 + 2z) + -2(z + 9) = 7(z + 1) (-1 * 6 + 2z * 6) + -2(z + 9) = 7(z + 1) (-6 + 12z) + -2(z + 9) = 7(z + 1) Reorder the terms: -6 + 12z + -2(9 + z) = 7(z + 1) -6 + 12z + (9 * -2 + z * -2) = 7(z + 1) -6 + 12z + (-18 + -2z) = 7(z + 1) Reorder the terms: -6 + -18 + 12z + -2z = 7(z + 1) Combine like terms: -6 + -18 = -24 -24 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -24 + 10z = 7(z + 1) Reorder the terms: -24 + 10z = 7(1 + z) -24 + 10z = (1 * 7 + z * 7) -24 + 10z = (7 + 7z) Solving -24 + 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. -24 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -24 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -24 + 3z = 7 + 0 -24 + 3z = 7 Add '24' to each side of the equation. -24 + 24 + 3z = 7 + 24 Combine like terms: -24 + 24 = 0 0 + 3z = 7 + 24 3z = 7 + 24 Combine like terms: 7 + 24 = 31 3z = 31 Divide each side by '3'. z = 10.33333333 Simplifying z = 10.33333333
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