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Simplifying 5(3z + -1) + -3(z + 2) = 7(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 2) = 7(z + 1) (-1 * 5 + 3z * 5) + -3(z + 2) = 7(z + 1) (-5 + 15z) + -3(z + 2) = 7(z + 1) Reorder the terms: -5 + 15z + -3(2 + z) = 7(z + 1) -5 + 15z + (2 * -3 + z * -3) = 7(z + 1) -5 + 15z + (-6 + -3z) = 7(z + 1) Reorder the terms: -5 + -6 + 15z + -3z = 7(z + 1) Combine like terms: -5 + -6 = -11 -11 + 15z + -3z = 7(z + 1) Combine like terms: 15z + -3z = 12z -11 + 12z = 7(z + 1) Reorder the terms: -11 + 12z = 7(1 + z) -11 + 12z = (1 * 7 + z * 7) -11 + 12z = (7 + 7z) Solving -11 + 12z = 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. -11 + 12z + -7z = 7 + 7z + -7z Combine like terms: 12z + -7z = 5z -11 + 5z = 7 + 7z + -7z Combine like terms: 7z + -7z = 0 -11 + 5z = 7 + 0 -11 + 5z = 7 Add '11' to each side of the equation. -11 + 11 + 5z = 7 + 11 Combine like terms: -11 + 11 = 0 0 + 5z = 7 + 11 5z = 7 + 11 Combine like terms: 7 + 11 = 18 5z = 18 Divide each side by '5'. z = 3.6 Simplifying z = 3.6
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