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Simplifying 3(4z + -1) + -4(z + 2) = 3(z + 1) Reorder the terms: 3(-1 + 4z) + -4(z + 2) = 3(z + 1) (-1 * 3 + 4z * 3) + -4(z + 2) = 3(z + 1) (-3 + 12z) + -4(z + 2) = 3(z + 1) Reorder the terms: -3 + 12z + -4(2 + z) = 3(z + 1) -3 + 12z + (2 * -4 + z * -4) = 3(z + 1) -3 + 12z + (-8 + -4z) = 3(z + 1) Reorder the terms: -3 + -8 + 12z + -4z = 3(z + 1) Combine like terms: -3 + -8 = -11 -11 + 12z + -4z = 3(z + 1) Combine like terms: 12z + -4z = 8z -11 + 8z = 3(z + 1) Reorder the terms: -11 + 8z = 3(1 + z) -11 + 8z = (1 * 3 + z * 3) -11 + 8z = (3 + 3z) Solving -11 + 8z = 3 + 3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-3z' to each side of the equation. -11 + 8z + -3z = 3 + 3z + -3z Combine like terms: 8z + -3z = 5z -11 + 5z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -11 + 5z = 3 + 0 -11 + 5z = 3 Add '11' to each side of the equation. -11 + 11 + 5z = 3 + 11 Combine like terms: -11 + 11 = 0 0 + 5z = 3 + 11 5z = 3 + 11 Combine like terms: 3 + 11 = 14 5z = 14 Divide each side by '5'. z = 2.8 Simplifying z = 2.8
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