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Simplifying 4(z + 2) = 2(4 + -1z) + 42 Reorder the terms: 4(2 + z) = 2(4 + -1z) + 42 (2 * 4 + z * 4) = 2(4 + -1z) + 42 (8 + 4z) = 2(4 + -1z) + 42 8 + 4z = (4 * 2 + -1z * 2) + 42 8 + 4z = (8 + -2z) + 42 Reorder the terms: 8 + 4z = 8 + 42 + -2z Combine like terms: 8 + 42 = 50 8 + 4z = 50 + -2z Solving 8 + 4z = 50 + -2z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2z' to each side of the equation. 8 + 4z + 2z = 50 + -2z + 2z Combine like terms: 4z + 2z = 6z 8 + 6z = 50 + -2z + 2z Combine like terms: -2z + 2z = 0 8 + 6z = 50 + 0 8 + 6z = 50 Add '-8' to each side of the equation. 8 + -8 + 6z = 50 + -8 Combine like terms: 8 + -8 = 0 0 + 6z = 50 + -8 6z = 50 + -8 Combine like terms: 50 + -8 = 42 6z = 42 Divide each side by '6'. z = 7 Simplifying z = 7
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