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Simplifying 6(3z + -1) + -3(z + 4) = 7(z + 1) Reorder the terms: 6(-1 + 3z) + -3(z + 4) = 7(z + 1) (-1 * 6 + 3z * 6) + -3(z + 4) = 7(z + 1) (-6 + 18z) + -3(z + 4) = 7(z + 1) Reorder the terms: -6 + 18z + -3(4 + z) = 7(z + 1) -6 + 18z + (4 * -3 + z * -3) = 7(z + 1) -6 + 18z + (-12 + -3z) = 7(z + 1) Reorder the terms: -6 + -12 + 18z + -3z = 7(z + 1) Combine like terms: -6 + -12 = -18 -18 + 18z + -3z = 7(z + 1) Combine like terms: 18z + -3z = 15z -18 + 15z = 7(z + 1) Reorder the terms: -18 + 15z = 7(1 + z) -18 + 15z = (1 * 7 + z * 7) -18 + 15z = (7 + 7z) Solving -18 + 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. -18 + 15z + -7z = 7 + 7z + -7z Combine like terms: 15z + -7z = 8z -18 + 8z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -18 + 8z = 7 + 0 -18 + 8z = 7 Add '18' to each side of the equation. -18 + 18 + 8z = 7 + 18 Combine like terms: -18 + 18 = 0 0 + 8z = 7 + 18 8z = 7 + 18 Combine like terms: 7 + 18 = 25 8z = 25 Divide each side by '8'. z = 3.125 Simplifying z = 3.125
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