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Simplifying -1[-5z + (13z + 7)] = 7(7z + 6) Reorder the terms: -1[-5z + (7 + 13z)] = 7(7z + 6) Remove parenthesis around (7 + 13z) -1[-5z + 7 + 13z] = 7(7z + 6) Reorder the terms: -1[7 + -5z + 13z] = 7(7z + 6) Combine like terms: -5z + 13z = 8z -1[7 + 8z] = 7(7z + 6) [7 * -1 + 8z * -1] = 7(7z + 6) [-7 + -8z] = 7(7z + 6) Reorder the terms: -7 + -8z = 7(6 + 7z) -7 + -8z = (6 * 7 + 7z * 7) -7 + -8z = (42 + 49z) Solving -7 + -8z = 42 + 49z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-49z' to each side of the equation. -7 + -8z + -49z = 42 + 49z + -49z Combine like terms: -8z + -49z = -57z -7 + -57z = 42 + 49z + -49z Combine like terms: 49z + -49z = 0 -7 + -57z = 42 + 0 -7 + -57z = 42 Add '7' to each side of the equation. -7 + 7 + -57z = 42 + 7 Combine like terms: -7 + 7 = 0 0 + -57z = 42 + 7 -57z = 42 + 7 Combine like terms: 42 + 7 = 49 -57z = 49 Divide each side by '-57'. z = -0.8596491228 Simplifying z = -0.8596491228
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