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Simplifying -1(4z + -1(10z + 1)) = 1 + (5z + 2) Reorder the terms: -1(4z + -1(1 + 10z)) = 1 + (5z + 2) -1(4z + (1 * -1 + 10z * -1)) = 1 + (5z + 2) -1(4z + (-1 + -10z)) = 1 + (5z + 2) Reorder the terms: -1(-1 + 4z + -10z) = 1 + (5z + 2) Combine like terms: 4z + -10z = -6z -1(-1 + -6z) = 1 + (5z + 2) (-1 * -1 + -6z * -1) = 1 + (5z + 2) (1 + 6z) = 1 + (5z + 2) Reorder the terms: 1 + 6z = 1 + (2 + 5z) Remove parenthesis around (2 + 5z) 1 + 6z = 1 + 2 + 5z Combine like terms: 1 + 2 = 3 1 + 6z = 3 + 5z Solving 1 + 6z = 3 + 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. 1 + 6z + -5z = 3 + 5z + -5z Combine like terms: 6z + -5z = 1z 1 + 1z = 3 + 5z + -5z Combine like terms: 5z + -5z = 0 1 + 1z = 3 + 0 1 + 1z = 3 Add '-1' to each side of the equation. 1 + -1 + 1z = 3 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 3 + -1 1z = 3 + -1 Combine like terms: 3 + -1 = 2 1z = 2 Divide each side by '1'. z = 2 Simplifying z = 2
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