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Simplifying 3(5z + -1) + -5(z + 8) = 8(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 8) = 8(z + 1) (-1 * 3 + 5z * 3) + -5(z + 8) = 8(z + 1) (-3 + 15z) + -5(z + 8) = 8(z + 1) Reorder the terms: -3 + 15z + -5(8 + z) = 8(z + 1) -3 + 15z + (8 * -5 + z * -5) = 8(z + 1) -3 + 15z + (-40 + -5z) = 8(z + 1) Reorder the terms: -3 + -40 + 15z + -5z = 8(z + 1) Combine like terms: -3 + -40 = -43 -43 + 15z + -5z = 8(z + 1) Combine like terms: 15z + -5z = 10z -43 + 10z = 8(z + 1) Reorder the terms: -43 + 10z = 8(1 + z) -43 + 10z = (1 * 8 + z * 8) -43 + 10z = (8 + 8z) Solving -43 + 10z = 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. -43 + 10z + -8z = 8 + 8z + -8z Combine like terms: 10z + -8z = 2z -43 + 2z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -43 + 2z = 8 + 0 -43 + 2z = 8 Add '43' to each side of the equation. -43 + 43 + 2z = 8 + 43 Combine like terms: -43 + 43 = 0 0 + 2z = 8 + 43 2z = 8 + 43 Combine like terms: 8 + 43 = 51 2z = 51 Divide each side by '2'. z = 25.5 Simplifying z = 25.5
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