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Simplifying 6(2z + -1) + -3(z + 4) = 7(z + 1) Reorder the terms: 6(-1 + 2z) + -3(z + 4) = 7(z + 1) (-1 * 6 + 2z * 6) + -3(z + 4) = 7(z + 1) (-6 + 12z) + -3(z + 4) = 7(z + 1) Reorder the terms: -6 + 12z + -3(4 + z) = 7(z + 1) -6 + 12z + (4 * -3 + z * -3) = 7(z + 1) -6 + 12z + (-12 + -3z) = 7(z + 1) Reorder the terms: -6 + -12 + 12z + -3z = 7(z + 1) Combine like terms: -6 + -12 = -18 -18 + 12z + -3z = 7(z + 1) Combine like terms: 12z + -3z = 9z -18 + 9z = 7(z + 1) Reorder the terms: -18 + 9z = 7(1 + z) -18 + 9z = (1 * 7 + z * 7) -18 + 9z = (7 + 7z) Solving -18 + 9z = 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. -18 + 9z + -7z = 7 + 7z + -7z Combine like terms: 9z + -7z = 2z -18 + 2z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -18 + 2z = 7 + 0 -18 + 2z = 7 Add '18' to each side of the equation. -18 + 18 + 2z = 7 + 18 Combine like terms: -18 + 18 = 0 0 + 2z = 7 + 18 2z = 7 + 18 Combine like terms: 7 + 18 = 25 2z = 25 Divide each side by '2'. z = 12.5 Simplifying z = 12.5
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