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Simplifying 3(4z + -1) + -4(z + 6) = 5(z + 1) Reorder the terms: 3(-1 + 4z) + -4(z + 6) = 5(z + 1) (-1 * 3 + 4z * 3) + -4(z + 6) = 5(z + 1) (-3 + 12z) + -4(z + 6) = 5(z + 1) Reorder the terms: -3 + 12z + -4(6 + z) = 5(z + 1) -3 + 12z + (6 * -4 + z * -4) = 5(z + 1) -3 + 12z + (-24 + -4z) = 5(z + 1) Reorder the terms: -3 + -24 + 12z + -4z = 5(z + 1) Combine like terms: -3 + -24 = -27 -27 + 12z + -4z = 5(z + 1) Combine like terms: 12z + -4z = 8z -27 + 8z = 5(z + 1) Reorder the terms: -27 + 8z = 5(1 + z) -27 + 8z = (1 * 5 + z * 5) -27 + 8z = (5 + 5z) Solving -27 + 8z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -27 + 8z + -5z = 5 + 5z + -5z Combine like terms: 8z + -5z = 3z -27 + 3z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -27 + 3z = 5 + 0 -27 + 3z = 5 Add '27' to each side of the equation. -27 + 27 + 3z = 5 + 27 Combine like terms: -27 + 27 = 0 0 + 3z = 5 + 27 3z = 5 + 27 Combine like terms: 5 + 27 = 32 3z = 32 Divide each side by '3'. z = 10.66666667 Simplifying z = 10.66666667
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