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Simplifying 4(5z + -1) + -4(z + 6) = 7(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 6) = 7(z + 1) (-1 * 4 + 5z * 4) + -4(z + 6) = 7(z + 1) (-4 + 20z) + -4(z + 6) = 7(z + 1) Reorder the terms: -4 + 20z + -4(6 + z) = 7(z + 1) -4 + 20z + (6 * -4 + z * -4) = 7(z + 1) -4 + 20z + (-24 + -4z) = 7(z + 1) Reorder the terms: -4 + -24 + 20z + -4z = 7(z + 1) Combine like terms: -4 + -24 = -28 -28 + 20z + -4z = 7(z + 1) Combine like terms: 20z + -4z = 16z -28 + 16z = 7(z + 1) Reorder the terms: -28 + 16z = 7(1 + z) -28 + 16z = (1 * 7 + z * 7) -28 + 16z = (7 + 7z) Solving -28 + 16z = 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. -28 + 16z + -7z = 7 + 7z + -7z Combine like terms: 16z + -7z = 9z -28 + 9z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -28 + 9z = 7 + 0 -28 + 9z = 7 Add '28' to each side of the equation. -28 + 28 + 9z = 7 + 28 Combine like terms: -28 + 28 = 0 0 + 9z = 7 + 28 9z = 7 + 28 Combine like terms: 7 + 28 = 35 9z = 35 Divide each side by '9'. z = 3.888888889 Simplifying z = 3.888888889
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