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Simplifying 5(3z + -1) + -5(z + 2) = 3(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 2) = 3(z + 1) (-1 * 5 + 3z * 5) + -5(z + 2) = 3(z + 1) (-5 + 15z) + -5(z + 2) = 3(z + 1) Reorder the terms: -5 + 15z + -5(2 + z) = 3(z + 1) -5 + 15z + (2 * -5 + z * -5) = 3(z + 1) -5 + 15z + (-10 + -5z) = 3(z + 1) Reorder the terms: -5 + -10 + 15z + -5z = 3(z + 1) Combine like terms: -5 + -10 = -15 -15 + 15z + -5z = 3(z + 1) Combine like terms: 15z + -5z = 10z -15 + 10z = 3(z + 1) Reorder the terms: -15 + 10z = 3(1 + z) -15 + 10z = (1 * 3 + z * 3) -15 + 10z = (3 + 3z) Solving -15 + 10z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -15 + 10z + -3z = 3 + 3z + -3z Combine like terms: 10z + -3z = 7z -15 + 7z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -15 + 7z = 3 + 0 -15 + 7z = 3 Add '15' to each side of the equation. -15 + 15 + 7z = 3 + 15 Combine like terms: -15 + 15 = 0 0 + 7z = 3 + 15 7z = 3 + 15 Combine like terms: 3 + 15 = 18 7z = 18 Divide each side by '7'. z = 2.571428571 Simplifying z = 2.571428571
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