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Simplifying 5(3z + -1) + -5(z + 5) = 7(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 5) = 7(z + 1) (-1 * 5 + 3z * 5) + -5(z + 5) = 7(z + 1) (-5 + 15z) + -5(z + 5) = 7(z + 1) Reorder the terms: -5 + 15z + -5(5 + z) = 7(z + 1) -5 + 15z + (5 * -5 + z * -5) = 7(z + 1) -5 + 15z + (-25 + -5z) = 7(z + 1) Reorder the terms: -5 + -25 + 15z + -5z = 7(z + 1) Combine like terms: -5 + -25 = -30 -30 + 15z + -5z = 7(z + 1) Combine like terms: 15z + -5z = 10z -30 + 10z = 7(z + 1) Reorder the terms: -30 + 10z = 7(1 + z) -30 + 10z = (1 * 7 + z * 7) -30 + 10z = (7 + 7z) Solving -30 + 10z = 7 + 7z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7z' to each side of the equation. -30 + 10z + -7z = 7 + 7z + -7z Combine like terms: 10z + -7z = 3z -30 + 3z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -30 + 3z = 7 + 0 -30 + 3z = 7 Add '30' to each side of the equation. -30 + 30 + 3z = 7 + 30 Combine like terms: -30 + 30 = 0 0 + 3z = 7 + 30 3z = 7 + 30 Combine like terms: 7 + 30 = 37 3z = 37 Divide each side by '3'. z = 12.33333333 Simplifying z = 12.33333333
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