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Simplifying 5(3z + -1) + -3(z + 1) = 3(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 1) = 3(z + 1) (-1 * 5 + 3z * 5) + -3(z + 1) = 3(z + 1) (-5 + 15z) + -3(z + 1) = 3(z + 1) Reorder the terms: -5 + 15z + -3(1 + z) = 3(z + 1) -5 + 15z + (1 * -3 + z * -3) = 3(z + 1) -5 + 15z + (-3 + -3z) = 3(z + 1) Reorder the terms: -5 + -3 + 15z + -3z = 3(z + 1) Combine like terms: -5 + -3 = -8 -8 + 15z + -3z = 3(z + 1) Combine like terms: 15z + -3z = 12z -8 + 12z = 3(z + 1) Reorder the terms: -8 + 12z = 3(1 + z) -8 + 12z = (1 * 3 + z * 3) -8 + 12z = (3 + 3z) Solving -8 + 12z = 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 + 12z + -3z = 3 + 3z + -3z Combine like terms: 12z + -3z = 9z -8 + 9z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -8 + 9z = 3 + 0 -8 + 9z = 3 Add '8' to each side of the equation. -8 + 8 + 9z = 3 + 8 Combine like terms: -8 + 8 = 0 0 + 9z = 3 + 8 9z = 3 + 8 Combine like terms: 3 + 8 = 11 9z = 11 Divide each side by '9'. z = 1.222222222 Simplifying z = 1.222222222
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