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Simplifying 6(2z + -1) + -5(z + 2) = 5(z + 1) Reorder the terms: 6(-1 + 2z) + -5(z + 2) = 5(z + 1) (-1 * 6 + 2z * 6) + -5(z + 2) = 5(z + 1) (-6 + 12z) + -5(z + 2) = 5(z + 1) Reorder the terms: -6 + 12z + -5(2 + z) = 5(z + 1) -6 + 12z + (2 * -5 + z * -5) = 5(z + 1) -6 + 12z + (-10 + -5z) = 5(z + 1) Reorder the terms: -6 + -10 + 12z + -5z = 5(z + 1) Combine like terms: -6 + -10 = -16 -16 + 12z + -5z = 5(z + 1) Combine like terms: 12z + -5z = 7z -16 + 7z = 5(z + 1) Reorder the terms: -16 + 7z = 5(1 + z) -16 + 7z = (1 * 5 + z * 5) -16 + 7z = (5 + 5z) Solving -16 + 7z = 5 + 5z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-5z' to each side of the equation. -16 + 7z + -5z = 5 + 5z + -5z Combine like terms: 7z + -5z = 2z -16 + 2z = 5 + 5z + -5z Combine like terms: 5z + -5z = 0 -16 + 2z = 5 + 0 -16 + 2z = 5 Add '16' to each side of the equation. -16 + 16 + 2z = 5 + 16 Combine like terms: -16 + 16 = 0 0 + 2z = 5 + 16 2z = 5 + 16 Combine like terms: 5 + 16 = 21 2z = 21 Divide each side by '2'. z = 10.5 Simplifying z = 10.5
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