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Simplifying -1[10z + -1(19z + 7)] = 7 + (8z + 3) Reorder the terms: -1[10z + -1(7 + 19z)] = 7 + (8z + 3) -1[10z + (7 * -1 + 19z * -1)] = 7 + (8z + 3) -1[10z + (-7 + -19z)] = 7 + (8z + 3) Reorder the terms: -1[-7 + 10z + -19z] = 7 + (8z + 3) Combine like terms: 10z + -19z = -9z -1[-7 + -9z] = 7 + (8z + 3) [-7 * -1 + -9z * -1] = 7 + (8z + 3) [7 + 9z] = 7 + (8z + 3) Reorder the terms: 7 + 9z = 7 + (3 + 8z) Remove parenthesis around (3 + 8z) 7 + 9z = 7 + 3 + 8z Combine like terms: 7 + 3 = 10 7 + 9z = 10 + 8z Solving 7 + 9z = 10 + 8z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8z' to each side of the equation. 7 + 9z + -8z = 10 + 8z + -8z Combine like terms: 9z + -8z = 1z 7 + 1z = 10 + 8z + -8z Combine like terms: 8z + -8z = 0 7 + 1z = 10 + 0 7 + 1z = 10 Add '-7' to each side of the equation. 7 + -7 + 1z = 10 + -7 Combine like terms: 7 + -7 = 0 0 + 1z = 10 + -7 1z = 10 + -7 Combine like terms: 10 + -7 = 3 1z = 3 Divide each side by '1'. z = 3 Simplifying z = 3
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