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Simplifying 6(3z + -1) + -3(z + 8) = 11(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 8) = 11(z + 1) (-1 * 6 + 3z * 6) + -3(z + 8) = 11(z + 1) (-6 + 18z) + -3(z + 8) = 11(z + 1) Reorder the terms: -6 + 18z + -3(8 + z) = 11(z + 1) -6 + 18z + (8 * -3 + z * -3) = 11(z + 1) -6 + 18z + (-24 + -3z) = 11(z + 1) Reorder the terms: -6 + -24 + 18z + -3z = 11(z + 1) Combine like terms: -6 + -24 = -30 -30 + 18z + -3z = 11(z + 1) Combine like terms: 18z + -3z = 15z -30 + 15z = 11(z + 1) Reorder the terms: -30 + 15z = 11(1 + z) -30 + 15z = (1 * 11 + z * 11) -30 + 15z = (11 + 11z) Solving -30 + 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. -30 + 15z + -11z = 11 + 11z + -11z Combine like terms: 15z + -11z = 4z -30 + 4z = 11 + 11z + -11z Combine like terms: 11z + -11z = 0 -30 + 4z = 11 + 0 -30 + 4z = 11 Add '30' to each side of the equation. -30 + 30 + 4z = 11 + 30 Combine like terms: -30 + 30 = 0 0 + 4z = 11 + 30 4z = 11 + 30 Combine like terms: 11 + 30 = 41 4z = 41 Divide each side by '4'. z = 10.25 Simplifying z = 10.25
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