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Simplifying -1[5z + -1(7z + 3)] = 3 + (1z + 4) Reorder the terms: -1[5z + -1(3 + 7z)] = 3 + (1z + 4) -1[5z + (3 * -1 + 7z * -1)] = 3 + (1z + 4) -1[5z + (-3 + -7z)] = 3 + (1z + 4) Reorder the terms: -1[-3 + 5z + -7z] = 3 + (1z + 4) Combine like terms: 5z + -7z = -2z -1[-3 + -2z] = 3 + (1z + 4) [-3 * -1 + -2z * -1] = 3 + (1z + 4) [3 + 2z] = 3 + (1z + 4) Reorder the terms: 3 + 2z = 3 + (4 + 1z) Remove parenthesis around (4 + 1z) 3 + 2z = 3 + 4 + 1z Combine like terms: 3 + 4 = 7 3 + 2z = 7 + 1z Solving 3 + 2z = 7 + 1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1z' to each side of the equation. 3 + 2z + -1z = 7 + 1z + -1z Combine like terms: 2z + -1z = 1z 3 + 1z = 7 + 1z + -1z Combine like terms: 1z + -1z = 0 3 + 1z = 7 + 0 3 + 1z = 7 Add '-3' to each side of the equation. 3 + -3 + 1z = 7 + -3 Combine like terms: 3 + -3 = 0 0 + 1z = 7 + -3 1z = 7 + -3 Combine like terms: 7 + -3 = 4 1z = 4 Divide each side by '1'. z = 4 Simplifying z = 4
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