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Simplifying 4(3z + -1) + -5(z + 7) = 4(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 7) = 4(z + 1) (-1 * 4 + 3z * 4) + -5(z + 7) = 4(z + 1) (-4 + 12z) + -5(z + 7) = 4(z + 1) Reorder the terms: -4 + 12z + -5(7 + z) = 4(z + 1) -4 + 12z + (7 * -5 + z * -5) = 4(z + 1) -4 + 12z + (-35 + -5z) = 4(z + 1) Reorder the terms: -4 + -35 + 12z + -5z = 4(z + 1) Combine like terms: -4 + -35 = -39 -39 + 12z + -5z = 4(z + 1) Combine like terms: 12z + -5z = 7z -39 + 7z = 4(z + 1) Reorder the terms: -39 + 7z = 4(1 + z) -39 + 7z = (1 * 4 + z * 4) -39 + 7z = (4 + 4z) Solving -39 + 7z = 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. -39 + 7z + -4z = 4 + 4z + -4z Combine like terms: 7z + -4z = 3z -39 + 3z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -39 + 3z = 4 + 0 -39 + 3z = 4 Add '39' to each side of the equation. -39 + 39 + 3z = 4 + 39 Combine like terms: -39 + 39 = 0 0 + 3z = 4 + 39 3z = 4 + 39 Combine like terms: 4 + 39 = 43 3z = 43 Divide each side by '3'. z = 14.33333333 Simplifying z = 14.33333333
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