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Simplifying 6(3z + -1) + -3(z + 7) = 4(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 7) = 4(z + 1) (-1 * 6 + 3z * 6) + -3(z + 7) = 4(z + 1) (-6 + 18z) + -3(z + 7) = 4(z + 1) Reorder the terms: -6 + 18z + -3(7 + z) = 4(z + 1) -6 + 18z + (7 * -3 + z * -3) = 4(z + 1) -6 + 18z + (-21 + -3z) = 4(z + 1) Reorder the terms: -6 + -21 + 18z + -3z = 4(z + 1) Combine like terms: -6 + -21 = -27 -27 + 18z + -3z = 4(z + 1) Combine like terms: 18z + -3z = 15z -27 + 15z = 4(z + 1) Reorder the terms: -27 + 15z = 4(1 + z) -27 + 15z = (1 * 4 + z * 4) -27 + 15z = (4 + 4z) Solving -27 + 15z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -27 + 15z + -4z = 4 + 4z + -4z Combine like terms: 15z + -4z = 11z -27 + 11z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -27 + 11z = 4 + 0 -27 + 11z = 4 Add '27' to each side of the equation. -27 + 27 + 11z = 4 + 27 Combine like terms: -27 + 27 = 0 0 + 11z = 4 + 27 11z = 4 + 27 Combine like terms: 4 + 27 = 31 11z = 31 Divide each side by '11'. z = 2.818181818 Simplifying z = 2.818181818
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