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Simplifying 4(5z + -1) + -4(z + 2) = 7(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 2) = 7(z + 1) (-1 * 4 + 5z * 4) + -4(z + 2) = 7(z + 1) (-4 + 20z) + -4(z + 2) = 7(z + 1) Reorder the terms: -4 + 20z + -4(2 + z) = 7(z + 1) -4 + 20z + (2 * -4 + z * -4) = 7(z + 1) -4 + 20z + (-8 + -4z) = 7(z + 1) Reorder the terms: -4 + -8 + 20z + -4z = 7(z + 1) Combine like terms: -4 + -8 = -12 -12 + 20z + -4z = 7(z + 1) Combine like terms: 20z + -4z = 16z -12 + 16z = 7(z + 1) Reorder the terms: -12 + 16z = 7(1 + z) -12 + 16z = (1 * 7 + z * 7) -12 + 16z = (7 + 7z) Solving -12 + 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. -12 + 16z + -7z = 7 + 7z + -7z Combine like terms: 16z + -7z = 9z -12 + 9z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -12 + 9z = 7 + 0 -12 + 9z = 7 Add '12' to each side of the equation. -12 + 12 + 9z = 7 + 12 Combine like terms: -12 + 12 = 0 0 + 9z = 7 + 12 9z = 7 + 12 Combine like terms: 7 + 12 = 19 9z = 19 Divide each side by '9'. z = 2.111111111 Simplifying z = 2.111111111
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