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Simplifying 4(3z + -1) + -5(z + 1) = 4(z + 1) Reorder the terms: 4(-1 + 3z) + -5(z + 1) = 4(z + 1) (-1 * 4 + 3z * 4) + -5(z + 1) = 4(z + 1) (-4 + 12z) + -5(z + 1) = 4(z + 1) Reorder the terms: -4 + 12z + -5(1 + z) = 4(z + 1) -4 + 12z + (1 * -5 + z * -5) = 4(z + 1) -4 + 12z + (-5 + -5z) = 4(z + 1) Reorder the terms: -4 + -5 + 12z + -5z = 4(z + 1) Combine like terms: -4 + -5 = -9 -9 + 12z + -5z = 4(z + 1) Combine like terms: 12z + -5z = 7z -9 + 7z = 4(z + 1) Reorder the terms: -9 + 7z = 4(1 + z) -9 + 7z = (1 * 4 + z * 4) -9 + 7z = (4 + 4z) Solving -9 + 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. -9 + 7z + -4z = 4 + 4z + -4z Combine like terms: 7z + -4z = 3z -9 + 3z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -9 + 3z = 4 + 0 -9 + 3z = 4 Add '9' to each side of the equation. -9 + 9 + 3z = 4 + 9 Combine like terms: -9 + 9 = 0 0 + 3z = 4 + 9 3z = 4 + 9 Combine like terms: 4 + 9 = 13 3z = 13 Divide each side by '3'. z = 4.333333333 Simplifying z = 4.333333333
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