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Simplifying 5(4z + -1) + -5(z + 9) = 9(z + 1) Reorder the terms: 5(-1 + 4z) + -5(z + 9) = 9(z + 1) (-1 * 5 + 4z * 5) + -5(z + 9) = 9(z + 1) (-5 + 20z) + -5(z + 9) = 9(z + 1) Reorder the terms: -5 + 20z + -5(9 + z) = 9(z + 1) -5 + 20z + (9 * -5 + z * -5) = 9(z + 1) -5 + 20z + (-45 + -5z) = 9(z + 1) Reorder the terms: -5 + -45 + 20z + -5z = 9(z + 1) Combine like terms: -5 + -45 = -50 -50 + 20z + -5z = 9(z + 1) Combine like terms: 20z + -5z = 15z -50 + 15z = 9(z + 1) Reorder the terms: -50 + 15z = 9(1 + z) -50 + 15z = (1 * 9 + z * 9) -50 + 15z = (9 + 9z) Solving -50 + 15z = 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. -50 + 15z + -9z = 9 + 9z + -9z Combine like terms: 15z + -9z = 6z -50 + 6z = 9 + 9z + -9z Combine like terms: 9z + -9z = 0 -50 + 6z = 9 + 0 -50 + 6z = 9 Add '50' to each side of the equation. -50 + 50 + 6z = 9 + 50 Combine like terms: -50 + 50 = 0 0 + 6z = 9 + 50 6z = 9 + 50 Combine like terms: 9 + 50 = 59 6z = 59 Divide each side by '6'. z = 9.833333333 Simplifying z = 9.833333333
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