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Simplifying 3(4z + -1) + -4(z + 7) = 3(z + 1) Reorder the terms: 3(-1 + 4z) + -4(z + 7) = 3(z + 1) (-1 * 3 + 4z * 3) + -4(z + 7) = 3(z + 1) (-3 + 12z) + -4(z + 7) = 3(z + 1) Reorder the terms: -3 + 12z + -4(7 + z) = 3(z + 1) -3 + 12z + (7 * -4 + z * -4) = 3(z + 1) -3 + 12z + (-28 + -4z) = 3(z + 1) Reorder the terms: -3 + -28 + 12z + -4z = 3(z + 1) Combine like terms: -3 + -28 = -31 -31 + 12z + -4z = 3(z + 1) Combine like terms: 12z + -4z = 8z -31 + 8z = 3(z + 1) Reorder the terms: -31 + 8z = 3(1 + z) -31 + 8z = (1 * 3 + z * 3) -31 + 8z = (3 + 3z) Solving -31 + 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. -31 + 8z + -3z = 3 + 3z + -3z Combine like terms: 8z + -3z = 5z -31 + 5z = 3 + 3z + -3z Combine like terms: 3z + -3z = 0 -31 + 5z = 3 + 0 -31 + 5z = 3 Add '31' to each side of the equation. -31 + 31 + 5z = 3 + 31 Combine like terms: -31 + 31 = 0 0 + 5z = 3 + 31 5z = 3 + 31 Combine like terms: 3 + 31 = 34 5z = 34 Divide each side by '5'. z = 6.8 Simplifying z = 6.8
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