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Simplifying 7 + 7(-1z + 6) = 5(-2z + 3) + -7 Reorder the terms: 7 + 7(6 + -1z) = 5(-2z + 3) + -7 7 + (6 * 7 + -1z * 7) = 5(-2z + 3) + -7 7 + (42 + -7z) = 5(-2z + 3) + -7 Combine like terms: 7 + 42 = 49 49 + -7z = 5(-2z + 3) + -7 Reorder the terms: 49 + -7z = 5(3 + -2z) + -7 49 + -7z = (3 * 5 + -2z * 5) + -7 49 + -7z = (15 + -10z) + -7 Reorder the terms: 49 + -7z = 15 + -7 + -10z Combine like terms: 15 + -7 = 8 49 + -7z = 8 + -10z Solving 49 + -7z = 8 + -10z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '10z' to each side of the equation. 49 + -7z + 10z = 8 + -10z + 10z Combine like terms: -7z + 10z = 3z 49 + 3z = 8 + -10z + 10z Combine like terms: -10z + 10z = 0 49 + 3z = 8 + 0 49 + 3z = 8 Add '-49' to each side of the equation. 49 + -49 + 3z = 8 + -49 Combine like terms: 49 + -49 = 0 0 + 3z = 8 + -49 3z = 8 + -49 Combine like terms: 8 + -49 = -41 3z = -41 Divide each side by '3'. z = -13.66666667 Simplifying z = -13.66666667
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