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Simplifying 6(3z + -1) + -5(z + 8) = 10(z + 1) Reorder the terms: 6(-1 + 3z) + -5(z + 8) = 10(z + 1) (-1 * 6 + 3z * 6) + -5(z + 8) = 10(z + 1) (-6 + 18z) + -5(z + 8) = 10(z + 1) Reorder the terms: -6 + 18z + -5(8 + z) = 10(z + 1) -6 + 18z + (8 * -5 + z * -5) = 10(z + 1) -6 + 18z + (-40 + -5z) = 10(z + 1) Reorder the terms: -6 + -40 + 18z + -5z = 10(z + 1) Combine like terms: -6 + -40 = -46 -46 + 18z + -5z = 10(z + 1) Combine like terms: 18z + -5z = 13z -46 + 13z = 10(z + 1) Reorder the terms: -46 + 13z = 10(1 + z) -46 + 13z = (1 * 10 + z * 10) -46 + 13z = (10 + 10z) Solving -46 + 13z = 10 + 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. -46 + 13z + -10z = 10 + 10z + -10z Combine like terms: 13z + -10z = 3z -46 + 3z = 10 + 10z + -10z Combine like terms: 10z + -10z = 0 -46 + 3z = 10 + 0 -46 + 3z = 10 Add '46' to each side of the equation. -46 + 46 + 3z = 10 + 46 Combine like terms: -46 + 46 = 0 0 + 3z = 10 + 46 3z = 10 + 46 Combine like terms: 10 + 46 = 56 3z = 56 Divide each side by '3'. z = 18.66666667 Simplifying z = 18.66666667
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