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Simplifying -2(5 + 7z) + -1 = 3(5z + 9(1 + -1z)) (5 * -2 + 7z * -2) + -1 = 3(5z + 9(1 + -1z)) (-10 + -14z) + -1 = 3(5z + 9(1 + -1z)) Reorder the terms: -10 + -1 + -14z = 3(5z + 9(1 + -1z)) Combine like terms: -10 + -1 = -11 -11 + -14z = 3(5z + 9(1 + -1z)) -11 + -14z = 3(5z + (1 * 9 + -1z * 9)) -11 + -14z = 3(5z + (9 + -9z)) Reorder the terms: -11 + -14z = 3(9 + 5z + -9z) Combine like terms: 5z + -9z = -4z -11 + -14z = 3(9 + -4z) -11 + -14z = (9 * 3 + -4z * 3) -11 + -14z = (27 + -12z) Solving -11 + -14z = 27 + -12z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '12z' to each side of the equation. -11 + -14z + 12z = 27 + -12z + 12z Combine like terms: -14z + 12z = -2z -11 + -2z = 27 + -12z + 12z Combine like terms: -12z + 12z = 0 -11 + -2z = 27 + 0 -11 + -2z = 27 Add '11' to each side of the equation. -11 + 11 + -2z = 27 + 11 Combine like terms: -11 + 11 = 0 0 + -2z = 27 + 11 -2z = 27 + 11 Combine like terms: 27 + 11 = 38 -2z = 38 Divide each side by '-2'. z = -19 Simplifying z = -19
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