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Simplifying 5(3z + -1) + -3(z + 2) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 2) = 8(z + 1) (-1 * 5 + 3z * 5) + -3(z + 2) = 8(z + 1) (-5 + 15z) + -3(z + 2) = 8(z + 1) Reorder the terms: -5 + 15z + -3(2 + z) = 8(z + 1) -5 + 15z + (2 * -3 + z * -3) = 8(z + 1) -5 + 15z + (-6 + -3z) = 8(z + 1) Reorder the terms: -5 + -6 + 15z + -3z = 8(z + 1) Combine like terms: -5 + -6 = -11 -11 + 15z + -3z = 8(z + 1) Combine like terms: 15z + -3z = 12z -11 + 12z = 8(z + 1) Reorder the terms: -11 + 12z = 8(1 + z) -11 + 12z = (1 * 8 + z * 8) -11 + 12z = (8 + 8z) Solving -11 + 12z = 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. -11 + 12z + -8z = 8 + 8z + -8z Combine like terms: 12z + -8z = 4z -11 + 4z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -11 + 4z = 8 + 0 -11 + 4z = 8 Add '11' to each side of the equation. -11 + 11 + 4z = 8 + 11 Combine like terms: -11 + 11 = 0 0 + 4z = 8 + 11 4z = 8 + 11 Combine like terms: 8 + 11 = 19 4z = 19 Divide each side by '4'. z = 4.75 Simplifying z = 4.75
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