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Simplifying 6(3z + -1) + -5(z + 5) = 8(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 5) = 8(z + 1) (-1 * 6 + 3z * 6) + -5(z + 5) = 8(z + 1) (-6 + 18z) + -5(z + 5) = 8(z + 1) Reorder the terms: -6 + 18z + -5(5 + z) = 8(z + 1) -6 + 18z + (5 * -5 + z * -5) = 8(z + 1) -6 + 18z + (-25 + -5z) = 8(z + 1) Reorder the terms: -6 + -25 + 18z + -5z = 8(z + 1) Combine like terms: -6 + -25 = -31 -31 + 18z + -5z = 8(z + 1) Combine like terms: 18z + -5z = 13z -31 + 13z = 8(z + 1) Reorder the terms: -31 + 13z = 8(1 + z) -31 + 13z = (1 * 8 + z * 8) -31 + 13z = (8 + 8z) Solving -31 + 13z = 8 + 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. -31 + 13z + -8z = 8 + 8z + -8z Combine like terms: 13z + -8z = 5z -31 + 5z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -31 + 5z = 8 + 0 -31 + 5z = 8 Add '31' to each side of the equation. -31 + 31 + 5z = 8 + 31 Combine like terms: -31 + 31 = 0 0 + 5z = 8 + 31 5z = 8 + 31 Combine like terms: 8 + 31 = 39 5z = 39 Divide each side by '5'. z = 7.8 Simplifying z = 7.8
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