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Simplifying 5(2z + -1) + -3(z + 3) = 5(z + 1) Reorder the terms: 5(-1 + 2z) + -3(z + 3) = 5(z + 1) (-1 * 5 + 2z * 5) + -3(z + 3) = 5(z + 1) (-5 + 10z) + -3(z + 3) = 5(z + 1) Reorder the terms: -5 + 10z + -3(3 + z) = 5(z + 1) -5 + 10z + (3 * -3 + z * -3) = 5(z + 1) -5 + 10z + (-9 + -3z) = 5(z + 1) Reorder the terms: -5 + -9 + 10z + -3z = 5(z + 1) Combine like terms: -5 + -9 = -14 -14 + 10z + -3z = 5(z + 1) Combine like terms: 10z + -3z = 7z -14 + 7z = 5(z + 1) Reorder the terms: -14 + 7z = 5(1 + z) -14 + 7z = (1 * 5 + z * 5) -14 + 7z = (5 + 5z) Solving -14 + 7z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -14 + 7z + -5z = 5 + 5z + -5z Combine like terms: 7z + -5z = 2z -14 + 2z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -14 + 2z = 5 + 0 -14 + 2z = 5 Add '14' to each side of the equation. -14 + 14 + 2z = 5 + 14 Combine like terms: -14 + 14 = 0 0 + 2z = 5 + 14 2z = 5 + 14 Combine like terms: 5 + 14 = 19 2z = 19 Divide each side by '2'. z = 9.5 Simplifying z = 9.5
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