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Simplifying 5(6z + -1) + -3(z + 5) = 17(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 5) = 17(z + 1) (-1 * 5 + 6z * 5) + -3(z + 5) = 17(z + 1) (-5 + 30z) + -3(z + 5) = 17(z + 1) Reorder the terms: -5 + 30z + -3(5 + z) = 17(z + 1) -5 + 30z + (5 * -3 + z * -3) = 17(z + 1) -5 + 30z + (-15 + -3z) = 17(z + 1) Reorder the terms: -5 + -15 + 30z + -3z = 17(z + 1) Combine like terms: -5 + -15 = -20 -20 + 30z + -3z = 17(z + 1) Combine like terms: 30z + -3z = 27z -20 + 27z = 17(z + 1) Reorder the terms: -20 + 27z = 17(1 + z) -20 + 27z = (1 * 17 + z * 17) -20 + 27z = (17 + 17z) Solving -20 + 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. -20 + 27z + -17z = 17 + 17z + -17z Combine like terms: 27z + -17z = 10z -20 + 10z = 17 + 17z + -17z Combine like terms: 17z + -17z = 0 -20 + 10z = 17 + 0 -20 + 10z = 17 Add '20' to each side of the equation. -20 + 20 + 10z = 17 + 20 Combine like terms: -20 + 20 = 0 0 + 10z = 17 + 20 10z = 17 + 20 Combine like terms: 17 + 20 = 37 10z = 37 Divide each side by '10'. z = 3.7 Simplifying z = 3.7
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