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Simplifying 5(3z + -1) + -3(z + 8) = 8(z + 1) Reorder the terms: 5(-1 + 3z) + -3(z + 8) = 8(z + 1) (-1 * 5 + 3z * 5) + -3(z + 8) = 8(z + 1) (-5 + 15z) + -3(z + 8) = 8(z + 1) Reorder the terms: -5 + 15z + -3(8 + z) = 8(z + 1) -5 + 15z + (8 * -3 + z * -3) = 8(z + 1) -5 + 15z + (-24 + -3z) = 8(z + 1) Reorder the terms: -5 + -24 + 15z + -3z = 8(z + 1) Combine like terms: -5 + -24 = -29 -29 + 15z + -3z = 8(z + 1) Combine like terms: 15z + -3z = 12z -29 + 12z = 8(z + 1) Reorder the terms: -29 + 12z = 8(1 + z) -29 + 12z = (1 * 8 + z * 8) -29 + 12z = (8 + 8z) Solving -29 + 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. -29 + 12z + -8z = 8 + 8z + -8z Combine like terms: 12z + -8z = 4z -29 + 4z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -29 + 4z = 8 + 0 -29 + 4z = 8 Add '29' to each side of the equation. -29 + 29 + 4z = 8 + 29 Combine like terms: -29 + 29 = 0 0 + 4z = 8 + 29 4z = 8 + 29 Combine like terms: 8 + 29 = 37 4z = 37 Divide each side by '4'. z = 9.25 Simplifying z = 9.25
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