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Simplifying 5(2z + -1) + -4(z + 9) = 4(z + 1) Reorder the terms: 5(-1 + 2z) + -4(z + 9) = 4(z + 1) (-1 * 5 + 2z * 5) + -4(z + 9) = 4(z + 1) (-5 + 10z) + -4(z + 9) = 4(z + 1) Reorder the terms: -5 + 10z + -4(9 + z) = 4(z + 1) -5 + 10z + (9 * -4 + z * -4) = 4(z + 1) -5 + 10z + (-36 + -4z) = 4(z + 1) Reorder the terms: -5 + -36 + 10z + -4z = 4(z + 1) Combine like terms: -5 + -36 = -41 -41 + 10z + -4z = 4(z + 1) Combine like terms: 10z + -4z = 6z -41 + 6z = 4(z + 1) Reorder the terms: -41 + 6z = 4(1 + z) -41 + 6z = (1 * 4 + z * 4) -41 + 6z = (4 + 4z) Solving -41 + 6z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -41 + 6z + -4z = 4 + 4z + -4z Combine like terms: 6z + -4z = 2z -41 + 2z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -41 + 2z = 4 + 0 -41 + 2z = 4 Add '41' to each side of the equation. -41 + 41 + 2z = 4 + 41 Combine like terms: -41 + 41 = 0 0 + 2z = 4 + 41 2z = 4 + 41 Combine like terms: 4 + 41 = 45 2z = 45 Divide each side by '2'. z = 22.5 Simplifying z = 22.5
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