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Simplifying 5(3z + -1) + -5(z + 8) = 3(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 8) = 3(z + 1) (-1 * 5 + 3z * 5) + -5(z + 8) = 3(z + 1) (-5 + 15z) + -5(z + 8) = 3(z + 1) Reorder the terms: -5 + 15z + -5(8 + z) = 3(z + 1) -5 + 15z + (8 * -5 + z * -5) = 3(z + 1) -5 + 15z + (-40 + -5z) = 3(z + 1) Reorder the terms: -5 + -40 + 15z + -5z = 3(z + 1) Combine like terms: -5 + -40 = -45 -45 + 15z + -5z = 3(z + 1) Combine like terms: 15z + -5z = 10z -45 + 10z = 3(z + 1) Reorder the terms: -45 + 10z = 3(1 + z) -45 + 10z = (1 * 3 + z * 3) -45 + 10z = (3 + 3z) Solving -45 + 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. -45 + 10z + -3z = 3 + 3z + -3z Combine like terms: 10z + -3z = 7z -45 + 7z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -45 + 7z = 3 + 0 -45 + 7z = 3 Add '45' to each side of the equation. -45 + 45 + 7z = 3 + 45 Combine like terms: -45 + 45 = 0 0 + 7z = 3 + 45 7z = 3 + 45 Combine like terms: 3 + 45 = 48 7z = 48 Divide each side by '7'. z = 6.857142857 Simplifying z = 6.857142857
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