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Simplifying 6(3z + -1) + -3(z + 4) = 8(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 4) = 8(z + 1) (-1 * 6 + 3z * 6) + -3(z + 4) = 8(z + 1) (-6 + 18z) + -3(z + 4) = 8(z + 1) Reorder the terms: -6 + 18z + -3(4 + z) = 8(z + 1) -6 + 18z + (4 * -3 + z * -3) = 8(z + 1) -6 + 18z + (-12 + -3z) = 8(z + 1) Reorder the terms: -6 + -12 + 18z + -3z = 8(z + 1) Combine like terms: -6 + -12 = -18 -18 + 18z + -3z = 8(z + 1) Combine like terms: 18z + -3z = 15z -18 + 15z = 8(z + 1) Reorder the terms: -18 + 15z = 8(1 + z) -18 + 15z = (1 * 8 + z * 8) -18 + 15z = (8 + 8z) Solving -18 + 15z = 8 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. -18 + 15z + -8z = 8 + 8z + -8z Combine like terms: 15z + -8z = 7z -18 + 7z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -18 + 7z = 8 + 0 -18 + 7z = 8 Add '18' to each side of the equation. -18 + 18 + 7z = 8 + 18 Combine like terms: -18 + 18 = 0 0 + 7z = 8 + 18 7z = 8 + 18 Combine like terms: 8 + 18 = 26 7z = 26 Divide each side by '7'. z = 3.714285714 Simplifying z = 3.714285714
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