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Simplifying 2(5z + -1) + -2(z + 6) = 3(z + 1) Reorder the terms: 2(-1 + 5z) + -2(z + 6) = 3(z + 1) (-1 * 2 + 5z * 2) + -2(z + 6) = 3(z + 1) (-2 + 10z) + -2(z + 6) = 3(z + 1) Reorder the terms: -2 + 10z + -2(6 + z) = 3(z + 1) -2 + 10z + (6 * -2 + z * -2) = 3(z + 1) -2 + 10z + (-12 + -2z) = 3(z + 1) Reorder the terms: -2 + -12 + 10z + -2z = 3(z + 1) Combine like terms: -2 + -12 = -14 -14 + 10z + -2z = 3(z + 1) Combine like terms: 10z + -2z = 8z -14 + 8z = 3(z + 1) Reorder the terms: -14 + 8z = 3(1 + z) -14 + 8z = (1 * 3 + z * 3) -14 + 8z = (3 + 3z) Solving -14 + 8z = 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. -14 + 8z + -3z = 3 + 3z + -3z Combine like terms: 8z + -3z = 5z -14 + 5z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -14 + 5z = 3 + 0 -14 + 5z = 3 Add '14' to each side of the equation. -14 + 14 + 5z = 3 + 14 Combine like terms: -14 + 14 = 0 0 + 5z = 3 + 14 5z = 3 + 14 Combine like terms: 3 + 14 = 17 5z = 17 Divide each side by '5'. z = 3.4 Simplifying z = 3.4
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