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Simplifying 5(4z + -1) + -4(z + 9) = 2(z + 1) Reorder the terms: 5(-1 + 4z) + -4(z + 9) = 2(z + 1) (-1 * 5 + 4z * 5) + -4(z + 9) = 2(z + 1) (-5 + 20z) + -4(z + 9) = 2(z + 1) Reorder the terms: -5 + 20z + -4(9 + z) = 2(z + 1) -5 + 20z + (9 * -4 + z * -4) = 2(z + 1) -5 + 20z + (-36 + -4z) = 2(z + 1) Reorder the terms: -5 + -36 + 20z + -4z = 2(z + 1) Combine like terms: -5 + -36 = -41 -41 + 20z + -4z = 2(z + 1) Combine like terms: 20z + -4z = 16z -41 + 16z = 2(z + 1) Reorder the terms: -41 + 16z = 2(1 + z) -41 + 16z = (1 * 2 + z * 2) -41 + 16z = (2 + 2z) Solving -41 + 16z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -41 + 16z + -2z = 2 + 2z + -2z Combine like terms: 16z + -2z = 14z -41 + 14z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -41 + 14z = 2 + 0 -41 + 14z = 2 Add '41' to each side of the equation. -41 + 41 + 14z = 2 + 41 Combine like terms: -41 + 41 = 0 0 + 14z = 2 + 41 14z = 2 + 41 Combine like terms: 2 + 41 = 43 14z = 43 Divide each side by '14'. z = 3.071428571 Simplifying z = 3.071428571
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