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Simplifying 5(4z + -1) + -5(z + 7) = 9(z + 2) Reorder the terms: 5(-1 + 4z) + -5(z + 7) = 9(z + 2) (-1 * 5 + 4z * 5) + -5(z + 7) = 9(z + 2) (-5 + 20z) + -5(z + 7) = 9(z + 2) Reorder the terms: -5 + 20z + -5(7 + z) = 9(z + 2) -5 + 20z + (7 * -5 + z * -5) = 9(z + 2) -5 + 20z + (-35 + -5z) = 9(z + 2) Reorder the terms: -5 + -35 + 20z + -5z = 9(z + 2) Combine like terms: -5 + -35 = -40 -40 + 20z + -5z = 9(z + 2) Combine like terms: 20z + -5z = 15z -40 + 15z = 9(z + 2) Reorder the terms: -40 + 15z = 9(2 + z) -40 + 15z = (2 * 9 + z * 9) -40 + 15z = (18 + 9z) Solving -40 + 15z = 18 + 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. -40 + 15z + -9z = 18 + 9z + -9z Combine like terms: 15z + -9z = 6z -40 + 6z = 18 + 9z + -9z Combine like terms: 9z + -9z = 0 -40 + 6z = 18 + 0 -40 + 6z = 18 Add '40' to each side of the equation. -40 + 40 + 6z = 18 + 40 Combine like terms: -40 + 40 = 0 0 + 6z = 18 + 40 6z = 18 + 40 Combine like terms: 18 + 40 = 58 6z = 58 Divide each side by '6'. z = 9.666666667 Simplifying z = 9.666666667
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