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Simplifying 3(5z + -1) + -5(z + 1) = 3(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 1) = 3(z + 1) (-1 * 3 + 5z * 3) + -5(z + 1) = 3(z + 1) (-3 + 15z) + -5(z + 1) = 3(z + 1) Reorder the terms: -3 + 15z + -5(1 + z) = 3(z + 1) -3 + 15z + (1 * -5 + z * -5) = 3(z + 1) -3 + 15z + (-5 + -5z) = 3(z + 1) Reorder the terms: -3 + -5 + 15z + -5z = 3(z + 1) Combine like terms: -3 + -5 = -8 -8 + 15z + -5z = 3(z + 1) Combine like terms: 15z + -5z = 10z -8 + 10z = 3(z + 1) Reorder the terms: -8 + 10z = 3(1 + z) -8 + 10z = (1 * 3 + z * 3) -8 + 10z = (3 + 3z) Solving -8 + 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. -8 + 10z + -3z = 3 + 3z + -3z Combine like terms: 10z + -3z = 7z -8 + 7z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -8 + 7z = 3 + 0 -8 + 7z = 3 Add '8' to each side of the equation. -8 + 8 + 7z = 3 + 8 Combine like terms: -8 + 8 = 0 0 + 7z = 3 + 8 7z = 3 + 8 Combine like terms: 3 + 8 = 11 7z = 11 Divide each side by '7'. z = 1.571428571 Simplifying z = 1.571428571
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