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Simplifying 4(5z + -1) + -4(z + 4) = 9(z + 1) Reorder the terms: 4(-1 + 5z) + -4(z + 4) = 9(z + 1) (-1 * 4 + 5z * 4) + -4(z + 4) = 9(z + 1) (-4 + 20z) + -4(z + 4) = 9(z + 1) Reorder the terms: -4 + 20z + -4(4 + z) = 9(z + 1) -4 + 20z + (4 * -4 + z * -4) = 9(z + 1) -4 + 20z + (-16 + -4z) = 9(z + 1) Reorder the terms: -4 + -16 + 20z + -4z = 9(z + 1) Combine like terms: -4 + -16 = -20 -20 + 20z + -4z = 9(z + 1) Combine like terms: 20z + -4z = 16z -20 + 16z = 9(z + 1) Reorder the terms: -20 + 16z = 9(1 + z) -20 + 16z = (1 * 9 + z * 9) -20 + 16z = (9 + 9z) Solving -20 + 16z = 9 + 9z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-9z' to each side of the equation. -20 + 16z + -9z = 9 + 9z + -9z Combine like terms: 16z + -9z = 7z -20 + 7z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -20 + 7z = 9 + 0 -20 + 7z = 9 Add '20' to each side of the equation. -20 + 20 + 7z = 9 + 20 Combine like terms: -20 + 20 = 0 0 + 7z = 9 + 20 7z = 9 + 20 Combine like terms: 9 + 20 = 29 7z = 29 Divide each side by '7'. z = 4.142857143 Simplifying z = 4.142857143
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