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Simplifying 6(3z + -1) + -3(z + 6) = 11(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 6) = 11(z + 1) (-1 * 6 + 3z * 6) + -3(z + 6) = 11(z + 1) (-6 + 18z) + -3(z + 6) = 11(z + 1) Reorder the terms: -6 + 18z + -3(6 + z) = 11(z + 1) -6 + 18z + (6 * -3 + z * -3) = 11(z + 1) -6 + 18z + (-18 + -3z) = 11(z + 1) Reorder the terms: -6 + -18 + 18z + -3z = 11(z + 1) Combine like terms: -6 + -18 = -24 -24 + 18z + -3z = 11(z + 1) Combine like terms: 18z + -3z = 15z -24 + 15z = 11(z + 1) Reorder the terms: -24 + 15z = 11(1 + z) -24 + 15z = (1 * 11 + z * 11) -24 + 15z = (11 + 11z) Solving -24 + 15z = 11 + 11z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-11z' to each side of the equation. -24 + 15z + -11z = 11 + 11z + -11z Combine like terms: 15z + -11z = 4z -24 + 4z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -24 + 4z = 11 + 0 -24 + 4z = 11 Add '24' to each side of the equation. -24 + 24 + 4z = 11 + 24 Combine like terms: -24 + 24 = 0 0 + 4z = 11 + 24 4z = 11 + 24 Combine like terms: 11 + 24 = 35 4z = 35 Divide each side by '4'. z = 8.75 Simplifying z = 8.75
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