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Simplifying 3(6z + -1) + -3(z + 7) = 7(z + 1) Reorder the terms: 3(-1 + 6z) + -3(z + 7) = 7(z + 1) (-1 * 3 + 6z * 3) + -3(z + 7) = 7(z + 1) (-3 + 18z) + -3(z + 7) = 7(z + 1) Reorder the terms: -3 + 18z + -3(7 + z) = 7(z + 1) -3 + 18z + (7 * -3 + z * -3) = 7(z + 1) -3 + 18z + (-21 + -3z) = 7(z + 1) Reorder the terms: -3 + -21 + 18z + -3z = 7(z + 1) Combine like terms: -3 + -21 = -24 -24 + 18z + -3z = 7(z + 1) Combine like terms: 18z + -3z = 15z -24 + 15z = 7(z + 1) Reorder the terms: -24 + 15z = 7(1 + z) -24 + 15z = (1 * 7 + z * 7) -24 + 15z = (7 + 7z) Solving -24 + 15z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -24 + 15z + -7z = 7 + 7z + -7z Combine like terms: 15z + -7z = 8z -24 + 8z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -24 + 8z = 7 + 0 -24 + 8z = 7 Add '24' to each side of the equation. -24 + 24 + 8z = 7 + 24 Combine like terms: -24 + 24 = 0 0 + 8z = 7 + 24 8z = 7 + 24 Combine like terms: 7 + 24 = 31 8z = 31 Divide each side by '8'. z = 3.875 Simplifying z = 3.875
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