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Simplifying 3(5z + -1) + -5(z + 9) = 3(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 9) = 3(z + 1) (-1 * 3 + 5z * 3) + -5(z + 9) = 3(z + 1) (-3 + 15z) + -5(z + 9) = 3(z + 1) Reorder the terms: -3 + 15z + -5(9 + z) = 3(z + 1) -3 + 15z + (9 * -5 + z * -5) = 3(z + 1) -3 + 15z + (-45 + -5z) = 3(z + 1) Reorder the terms: -3 + -45 + 15z + -5z = 3(z + 1) Combine like terms: -3 + -45 = -48 -48 + 15z + -5z = 3(z + 1) Combine like terms: 15z + -5z = 10z -48 + 10z = 3(z + 1) Reorder the terms: -48 + 10z = 3(1 + z) -48 + 10z = (1 * 3 + z * 3) -48 + 10z = (3 + 3z) Solving -48 + 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. -48 + 10z + -3z = 3 + 3z + -3z Combine like terms: 10z + -3z = 7z -48 + 7z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -48 + 7z = 3 + 0 -48 + 7z = 3 Add '48' to each side of the equation. -48 + 48 + 7z = 3 + 48 Combine like terms: -48 + 48 = 0 0 + 7z = 3 + 48 7z = 3 + 48 Combine like terms: 3 + 48 = 51 7z = 51 Divide each side by '7'. z = 7.285714286 Simplifying z = 7.285714286
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