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Simplifying 5(6z + -1) + -3(z + 3) = 17(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 3) = 17(z + 1) (-1 * 5 + 6z * 5) + -3(z + 3) = 17(z + 1) (-5 + 30z) + -3(z + 3) = 17(z + 1) Reorder the terms: -5 + 30z + -3(3 + z) = 17(z + 1) -5 + 30z + (3 * -3 + z * -3) = 17(z + 1) -5 + 30z + (-9 + -3z) = 17(z + 1) Reorder the terms: -5 + -9 + 30z + -3z = 17(z + 1) Combine like terms: -5 + -9 = -14 -14 + 30z + -3z = 17(z + 1) Combine like terms: 30z + -3z = 27z -14 + 27z = 17(z + 1) Reorder the terms: -14 + 27z = 17(1 + z) -14 + 27z = (1 * 17 + z * 17) -14 + 27z = (17 + 17z) Solving -14 + 27z = 17 + 17z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-17z' to each side of the equation. -14 + 27z + -17z = 17 + 17z + -17z Combine like terms: 27z + -17z = 10z -14 + 10z = 17 + 17z + -17z Combine like terms: 17z + -17z = 0 -14 + 10z = 17 + 0 -14 + 10z = 17 Add '14' to each side of the equation. -14 + 14 + 10z = 17 + 14 Combine like terms: -14 + 14 = 0 0 + 10z = 17 + 14 10z = 17 + 14 Combine like terms: 17 + 14 = 31 10z = 31 Divide each side by '10'. z = 3.1 Simplifying z = 3.1
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