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Simplifying 2(7z + -1) + -6(z + 3) = 5(z + 1) Reorder the terms: 2(-1 + 7z) + -6(z + 3) = 5(z + 1) (-1 * 2 + 7z * 2) + -6(z + 3) = 5(z + 1) (-2 + 14z) + -6(z + 3) = 5(z + 1) Reorder the terms: -2 + 14z + -6(3 + z) = 5(z + 1) -2 + 14z + (3 * -6 + z * -6) = 5(z + 1) -2 + 14z + (-18 + -6z) = 5(z + 1) Reorder the terms: -2 + -18 + 14z + -6z = 5(z + 1) Combine like terms: -2 + -18 = -20 -20 + 14z + -6z = 5(z + 1) Combine like terms: 14z + -6z = 8z -20 + 8z = 5(z + 1) Reorder the terms: -20 + 8z = 5(1 + z) -20 + 8z = (1 * 5 + z * 5) -20 + 8z = (5 + 5z) Solving -20 + 8z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -20 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -20 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -20 + 3z = 5 + 0 -20 + 3z = 5 Add '20' to each side of the equation. -20 + 20 + 3z = 5 + 20 Combine like terms: -20 + 20 = 0 0 + 3z = 5 + 20 3z = 5 + 20 Combine like terms: 5 + 20 = 25 3z = 25 Divide each side by '3'. z = 8.333333333 Simplifying z = 8.333333333
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