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Simplifying 2(3z + 4) + -1(2 + -8) = 3(4z + 2) + -7z + 10 Reorder the terms: 2(4 + 3z) + -1(2 + -8) = 3(4z + 2) + -7z + 10 (4 * 2 + 3z * 2) + -1(2 + -8) = 3(4z + 2) + -7z + 10 (8 + 6z) + -1(2 + -8) = 3(4z + 2) + -7z + 10 Combine like terms: 2 + -8 = -6 8 + 6z + -1(-6) = 3(4z + 2) + -7z + 10 Multiply -1 * -6 8 + 6z + 6 = 3(4z + 2) + -7z + 10 Reorder the terms: 8 + 6 + 6z = 3(4z + 2) + -7z + 10 Combine like terms: 8 + 6 = 14 14 + 6z = 3(4z + 2) + -7z + 10 Reorder the terms: 14 + 6z = 3(2 + 4z) + -7z + 10 14 + 6z = (2 * 3 + 4z * 3) + -7z + 10 14 + 6z = (6 + 12z) + -7z + 10 Reorder the terms: 14 + 6z = 6 + 10 + 12z + -7z Combine like terms: 6 + 10 = 16 14 + 6z = 16 + 12z + -7z Combine like terms: 12z + -7z = 5z 14 + 6z = 16 + 5z Solving 14 + 6z = 16 + 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. 14 + 6z + -5z = 16 + 5z + -5z Combine like terms: 6z + -5z = 1z 14 + 1z = 16 + 5z + -5z Combine like terms: 5z + -5z = 0 14 + 1z = 16 + 0 14 + 1z = 16 Add '-14' to each side of the equation. 14 + -14 + 1z = 16 + -14 Combine like terms: 14 + -14 = 0 0 + 1z = 16 + -14 1z = 16 + -14 Combine like terms: 16 + -14 = 2 1z = 2 Divide each side by '1'. z = 2 Simplifying z = 2
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