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Simplifying 6(5z + -1) + -5(z + 5) = 16(z + 1) Reorder the terms: 6(-1 + 5z) + -5(z + 5) = 16(z + 1) (-1 * 6 + 5z * 6) + -5(z + 5) = 16(z + 1) (-6 + 30z) + -5(z + 5) = 16(z + 1) Reorder the terms: -6 + 30z + -5(5 + z) = 16(z + 1) -6 + 30z + (5 * -5 + z * -5) = 16(z + 1) -6 + 30z + (-25 + -5z) = 16(z + 1) Reorder the terms: -6 + -25 + 30z + -5z = 16(z + 1) Combine like terms: -6 + -25 = -31 -31 + 30z + -5z = 16(z + 1) Combine like terms: 30z + -5z = 25z -31 + 25z = 16(z + 1) Reorder the terms: -31 + 25z = 16(1 + z) -31 + 25z = (1 * 16 + z * 16) -31 + 25z = (16 + 16z) Solving -31 + 25z = 16 + 16z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-16z' to each side of the equation. -31 + 25z + -16z = 16 + 16z + -16z Combine like terms: 25z + -16z = 9z -31 + 9z = 16 + 16z + -16z Combine like terms: 16z + -16z = 0 -31 + 9z = 16 + 0 -31 + 9z = 16 Add '31' to each side of the equation. -31 + 31 + 9z = 16 + 31 Combine like terms: -31 + 31 = 0 0 + 9z = 16 + 31 9z = 16 + 31 Combine like terms: 16 + 31 = 47 9z = 47 Divide each side by '9'. z = 5.222222222 Simplifying z = 5.222222222
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