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Simplifying -1[3z + -1(14z + 1)] = 1 + (10z + 4) Reorder the terms: -1[3z + -1(1 + 14z)] = 1 + (10z + 4) -1[3z + (1 * -1 + 14z * -1)] = 1 + (10z + 4) -1[3z + (-1 + -14z)] = 1 + (10z + 4) Reorder the terms: -1[-1 + 3z + -14z] = 1 + (10z + 4) Combine like terms: 3z + -14z = -11z -1[-1 + -11z] = 1 + (10z + 4) [-1 * -1 + -11z * -1] = 1 + (10z + 4) [1 + 11z] = 1 + (10z + 4) Reorder the terms: 1 + 11z = 1 + (4 + 10z) Remove parenthesis around (4 + 10z) 1 + 11z = 1 + 4 + 10z Combine like terms: 1 + 4 = 5 1 + 11z = 5 + 10z Solving 1 + 11z = 5 + 10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-10z' to each side of the equation. 1 + 11z + -10z = 5 + 10z + -10z Combine like terms: 11z + -10z = 1z 1 + 1z = 5 + 10z + -10z Combine like terms: 10z + -10z = 0 1 + 1z = 5 + 0 1 + 1z = 5 Add '-1' to each side of the equation. 1 + -1 + 1z = 5 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 5 + -1 1z = 5 + -1 Combine like terms: 5 + -1 = 4 1z = 4 Divide each side by '1'. z = 4 Simplifying z = 4
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