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Simplifying 2(6z + -1) + -2(z + 7) = 7(z + 1) Reorder the terms: 2(-1 + 6z) + -2(z + 7) = 7(z + 1) (-1 * 2 + 6z * 2) + -2(z + 7) = 7(z + 1) (-2 + 12z) + -2(z + 7) = 7(z + 1) Reorder the terms: -2 + 12z + -2(7 + z) = 7(z + 1) -2 + 12z + (7 * -2 + z * -2) = 7(z + 1) -2 + 12z + (-14 + -2z) = 7(z + 1) Reorder the terms: -2 + -14 + 12z + -2z = 7(z + 1) Combine like terms: -2 + -14 = -16 -16 + 12z + -2z = 7(z + 1) Combine like terms: 12z + -2z = 10z -16 + 10z = 7(z + 1) Reorder the terms: -16 + 10z = 7(1 + z) -16 + 10z = (1 * 7 + z * 7) -16 + 10z = (7 + 7z) Solving -16 + 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. -16 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -16 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -16 + 3z = 7 + 0 -16 + 3z = 7 Add '16' to each side of the equation. -16 + 16 + 3z = 7 + 16 Combine like terms: -16 + 16 = 0 0 + 3z = 7 + 16 3z = 7 + 16 Combine like terms: 7 + 16 = 23 3z = 23 Divide each side by '3'. z = 7.666666667 Simplifying z = 7.666666667
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