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Simplifying 2(5z + -1) + -2(z + 8) = 5(z + 1) Reorder the terms: 2(-1 + 5z) + -2(z + 8) = 5(z + 1) (-1 * 2 + 5z * 2) + -2(z + 8) = 5(z + 1) (-2 + 10z) + -2(z + 8) = 5(z + 1) Reorder the terms: -2 + 10z + -2(8 + z) = 5(z + 1) -2 + 10z + (8 * -2 + z * -2) = 5(z + 1) -2 + 10z + (-16 + -2z) = 5(z + 1) Reorder the terms: -2 + -16 + 10z + -2z = 5(z + 1) Combine like terms: -2 + -16 = -18 -18 + 10z + -2z = 5(z + 1) Combine like terms: 10z + -2z = 8z -18 + 8z = 5(z + 1) Reorder the terms: -18 + 8z = 5(1 + z) -18 + 8z = (1 * 5 + z * 5) -18 + 8z = (5 + 5z) Solving -18 + 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. -18 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -18 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -18 + 3z = 5 + 0 -18 + 3z = 5 Add '18' to each side of the equation. -18 + 18 + 3z = 5 + 18 Combine like terms: -18 + 18 = 0 0 + 3z = 5 + 18 3z = 5 + 18 Combine like terms: 5 + 18 = 23 3z = 23 Divide each side by '3'. z = 7.666666667 Simplifying z = 7.666666667
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