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Simplifying -1[5z + -1(9z + 1)] = 1 + (3z + 0) Reorder the terms: -1[5z + -1(1 + 9z)] = 1 + (3z + 0) -1[5z + (1 * -1 + 9z * -1)] = 1 + (3z + 0) -1[5z + (-1 + -9z)] = 1 + (3z + 0) Reorder the terms: -1[-1 + 5z + -9z] = 1 + (3z + 0) Combine like terms: 5z + -9z = -4z -1[-1 + -4z] = 1 + (3z + 0) [-1 * -1 + -4z * -1] = 1 + (3z + 0) [1 + 4z] = 1 + (3z + 0) Reorder the terms: 1 + 4z = 1 + (0 + 3z) Remove the zero: 1 + 4z = 1 + (3z) 1 + 4z = 1 + (3z) Add '-1' to each side of the equation. 1 + -1 + 4z = 1 + -1 + (3z) Combine like terms: 1 + -1 = 0 0 + 4z = 1 + -1 + (3z) 4z = 1 + -1 + (3z) Combine like terms: 1 + -1 = 0 4z = 0 + (3z) 4z = (3z) Solving 4z = (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. 4z + (-3z) = (3z) + (-3z) Combine like terms: 4z + (-3z) = 1z 1z = (3z) + (-3z) Combine like terms: (3z) + (-3z) = 0 1z = 0 Divide each side by '1'. z = 0 Simplifying z = 0
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