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Simplifying 5(2z + -1) + -3(z + 5) = 5(z + 1) Reorder the terms: 5(-1 + 2z) + -3(z + 5) = 5(z + 1) (-1 * 5 + 2z * 5) + -3(z + 5) = 5(z + 1) (-5 + 10z) + -3(z + 5) = 5(z + 1) Reorder the terms: -5 + 10z + -3(5 + z) = 5(z + 1) -5 + 10z + (5 * -3 + z * -3) = 5(z + 1) -5 + 10z + (-15 + -3z) = 5(z + 1) Reorder the terms: -5 + -15 + 10z + -3z = 5(z + 1) Combine like terms: -5 + -15 = -20 -20 + 10z + -3z = 5(z + 1) Combine like terms: 10z + -3z = 7z -20 + 7z = 5(z + 1) Reorder the terms: -20 + 7z = 5(1 + z) -20 + 7z = (1 * 5 + z * 5) -20 + 7z = (5 + 5z) Solving -20 + 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. -20 + 7z + -5z = 5 + 5z + -5z Combine like terms: 7z + -5z = 2z -20 + 2z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -20 + 2z = 5 + 0 -20 + 2z = 5 Add '20' to each side of the equation. -20 + 20 + 2z = 5 + 20 Combine like terms: -20 + 20 = 0 0 + 2z = 5 + 20 2z = 5 + 20 Combine like terms: 5 + 20 = 25 2z = 25 Divide each side by '2'. z = 12.5 Simplifying z = 12.5
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