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Simplifying 3(5z + -1) + -3(z + 2) = 4(z + 1) Reorder the terms: 3(-1 + 5z) + -3(z + 2) = 4(z + 1) (-1 * 3 + 5z * 3) + -3(z + 2) = 4(z + 1) (-3 + 15z) + -3(z + 2) = 4(z + 1) Reorder the terms: -3 + 15z + -3(2 + z) = 4(z + 1) -3 + 15z + (2 * -3 + z * -3) = 4(z + 1) -3 + 15z + (-6 + -3z) = 4(z + 1) Reorder the terms: -3 + -6 + 15z + -3z = 4(z + 1) Combine like terms: -3 + -6 = -9 -9 + 15z + -3z = 4(z + 1) Combine like terms: 15z + -3z = 12z -9 + 12z = 4(z + 1) Reorder the terms: -9 + 12z = 4(1 + z) -9 + 12z = (1 * 4 + z * 4) -9 + 12z = (4 + 4z) Solving -9 + 12z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -9 + 12z + -4z = 4 + 4z + -4z Combine like terms: 12z + -4z = 8z -9 + 8z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -9 + 8z = 4 + 0 -9 + 8z = 4 Add '9' to each side of the equation. -9 + 9 + 8z = 4 + 9 Combine like terms: -9 + 9 = 0 0 + 8z = 4 + 9 8z = 4 + 9 Combine like terms: 4 + 9 = 13 8z = 13 Divide each side by '8'. z = 1.625 Simplifying z = 1.625
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