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Simplifying 7(z + -5) = 6(z + 7) Reorder the terms: 7(-5 + z) = 6(z + 7) (-5 * 7 + z * 7) = 6(z + 7) (-35 + 7z) = 6(z + 7) Reorder the terms: -35 + 7z = 6(7 + z) -35 + 7z = (7 * 6 + z * 6) -35 + 7z = (42 + 6z) Solving -35 + 7z = 42 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -35 + 7z + -6z = 42 + 6z + -6z Combine like terms: 7z + -6z = 1z -35 + 1z = 42 + 6z + -6z Combine like terms: 6z + -6z = 0 -35 + 1z = 42 + 0 -35 + 1z = 42 Add '35' to each side of the equation. -35 + 35 + 1z = 42 + 35 Combine like terms: -35 + 35 = 0 0 + 1z = 42 + 35 1z = 42 + 35 Combine like terms: 42 + 35 = 77 1z = 77 Divide each side by '1'. z = 77 Simplifying z = 77
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