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Simplifying 4(3z + -1) + -5(z + 7) = 2(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 7) = 2(z + 1) (-1 * 4 + 3z * 4) + -5(z + 7) = 2(z + 1) (-4 + 12z) + -5(z + 7) = 2(z + 1) Reorder the terms: -4 + 12z + -5(7 + z) = 2(z + 1) -4 + 12z + (7 * -5 + z * -5) = 2(z + 1) -4 + 12z + (-35 + -5z) = 2(z + 1) Reorder the terms: -4 + -35 + 12z + -5z = 2(z + 1) Combine like terms: -4 + -35 = -39 -39 + 12z + -5z = 2(z + 1) Combine like terms: 12z + -5z = 7z -39 + 7z = 2(z + 1) Reorder the terms: -39 + 7z = 2(1 + z) -39 + 7z = (1 * 2 + z * 2) -39 + 7z = (2 + 2z) Solving -39 + 7z = 2 + 2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2z' to each side of the equation. -39 + 7z + -2z = 2 + 2z + -2z Combine like terms: 7z + -2z = 5z -39 + 5z = 2 + 2z + -2z Combine like terms: 2z + -2z = 0 -39 + 5z = 2 + 0 -39 + 5z = 2 Add '39' to each side of the equation. -39 + 39 + 5z = 2 + 39 Combine like terms: -39 + 39 = 0 0 + 5z = 2 + 39 5z = 2 + 39 Combine like terms: 2 + 39 = 41 5z = 41 Divide each side by '5'. z = 8.2 Simplifying z = 8.2
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