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Simplifying -1[4z + -1(7z + 1)] = 1 + (2z + 3) Reorder the terms: -1[4z + -1(1 + 7z)] = 1 + (2z + 3) -1[4z + (1 * -1 + 7z * -1)] = 1 + (2z + 3) -1[4z + (-1 + -7z)] = 1 + (2z + 3) Reorder the terms: -1[-1 + 4z + -7z] = 1 + (2z + 3) Combine like terms: 4z + -7z = -3z -1[-1 + -3z] = 1 + (2z + 3) [-1 * -1 + -3z * -1] = 1 + (2z + 3) [1 + 3z] = 1 + (2z + 3) Reorder the terms: 1 + 3z = 1 + (3 + 2z) Remove parenthesis around (3 + 2z) 1 + 3z = 1 + 3 + 2z Combine like terms: 1 + 3 = 4 1 + 3z = 4 + 2z Solving 1 + 3z = 4 + 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. 1 + 3z + -2z = 4 + 2z + -2z Combine like terms: 3z + -2z = 1z 1 + 1z = 4 + 2z + -2z Combine like terms: 2z + -2z = 0 1 + 1z = 4 + 0 1 + 1z = 4 Add '-1' to each side of the equation. 1 + -1 + 1z = 4 + -1 Combine like terms: 1 + -1 = 0 0 + 1z = 4 + -1 1z = 4 + -1 Combine like terms: 4 + -1 = 3 1z = 3 Divide each side by '1'. z = 3 Simplifying z = 3
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