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Simplifying 3(4z + -1) + -4(z + 4) = 6(z + 1) Reorder the terms: 3(-1 + 4z) + -4(z + 4) = 6(z + 1) (-1 * 3 + 4z * 3) + -4(z + 4) = 6(z + 1) (-3 + 12z) + -4(z + 4) = 6(z + 1) Reorder the terms: -3 + 12z + -4(4 + z) = 6(z + 1) -3 + 12z + (4 * -4 + z * -4) = 6(z + 1) -3 + 12z + (-16 + -4z) = 6(z + 1) Reorder the terms: -3 + -16 + 12z + -4z = 6(z + 1) Combine like terms: -3 + -16 = -19 -19 + 12z + -4z = 6(z + 1) Combine like terms: 12z + -4z = 8z -19 + 8z = 6(z + 1) Reorder the terms: -19 + 8z = 6(1 + z) -19 + 8z = (1 * 6 + z * 6) -19 + 8z = (6 + 6z) Solving -19 + 8z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -19 + 8z + -6z = 6 + 6z + -6z Combine like terms: 8z + -6z = 2z -19 + 2z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -19 + 2z = 6 + 0 -19 + 2z = 6 Add '19' to each side of the equation. -19 + 19 + 2z = 6 + 19 Combine like terms: -19 + 19 = 0 0 + 2z = 6 + 19 2z = 6 + 19 Combine like terms: 6 + 19 = 25 2z = 25 Divide each side by '2'. z = 12.5 Simplifying z = 12.5
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