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Simplifying 2(5z + -1) + -4(z + 8) = 3(z + 1) Reorder the terms: 2(-1 + 5z) + -4(z + 8) = 3(z + 1) (-1 * 2 + 5z * 2) + -4(z + 8) = 3(z + 1) (-2 + 10z) + -4(z + 8) = 3(z + 1) Reorder the terms: -2 + 10z + -4(8 + z) = 3(z + 1) -2 + 10z + (8 * -4 + z * -4) = 3(z + 1) -2 + 10z + (-32 + -4z) = 3(z + 1) Reorder the terms: -2 + -32 + 10z + -4z = 3(z + 1) Combine like terms: -2 + -32 = -34 -34 + 10z + -4z = 3(z + 1) Combine like terms: 10z + -4z = 6z -34 + 6z = 3(z + 1) Reorder the terms: -34 + 6z = 3(1 + z) -34 + 6z = (1 * 3 + z * 3) -34 + 6z = (3 + 3z) Solving -34 + 6z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -34 + 6z + -3z = 3 + 3z + -3z Combine like terms: 6z + -3z = 3z -34 + 3z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -34 + 3z = 3 + 0 -34 + 3z = 3 Add '34' to each side of the equation. -34 + 34 + 3z = 3 + 34 Combine like terms: -34 + 34 = 0 0 + 3z = 3 + 34 3z = 3 + 34 Combine like terms: 3 + 34 = 37 3z = 37 Divide each side by '3'. z = 12.33333333 Simplifying z = 12.33333333
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