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Simplifying 6(3z + -1) + -5(z + 1) = 6(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 1) = 6(z + 1) (-1 * 6 + 3z * 6) + -5(z + 1) = 6(z + 1) (-6 + 18z) + -5(z + 1) = 6(z + 1) Reorder the terms: -6 + 18z + -5(1 + z) = 6(z + 1) -6 + 18z + (1 * -5 + z * -5) = 6(z + 1) -6 + 18z + (-5 + -5z) = 6(z + 1) Reorder the terms: -6 + -5 + 18z + -5z = 6(z + 1) Combine like terms: -6 + -5 = -11 -11 + 18z + -5z = 6(z + 1) Combine like terms: 18z + -5z = 13z -11 + 13z = 6(z + 1) Reorder the terms: -11 + 13z = 6(1 + z) -11 + 13z = (1 * 6 + z * 6) -11 + 13z = (6 + 6z) Solving -11 + 13z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -11 + 13z + -6z = 6 + 6z + -6z Combine like terms: 13z + -6z = 7z -11 + 7z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -11 + 7z = 6 + 0 -11 + 7z = 6 Add '11' to each side of the equation. -11 + 11 + 7z = 6 + 11 Combine like terms: -11 + 11 = 0 0 + 7z = 6 + 11 7z = 6 + 11 Combine like terms: 6 + 11 = 17 7z = 17 Divide each side by '7'. z = 2.428571429 Simplifying z = 2.428571429
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