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Simplifying 3(5z + -1) + -4(z + 9) = 8(z + 1) Reorder the terms: 3(-1 + 5z) + -4(z + 9) = 8(z + 1) (-1 * 3 + 5z * 3) + -4(z + 9) = 8(z + 1) (-3 + 15z) + -4(z + 9) = 8(z + 1) Reorder the terms: -3 + 15z + -4(9 + z) = 8(z + 1) -3 + 15z + (9 * -4 + z * -4) = 8(z + 1) -3 + 15z + (-36 + -4z) = 8(z + 1) Reorder the terms: -3 + -36 + 15z + -4z = 8(z + 1) Combine like terms: -3 + -36 = -39 -39 + 15z + -4z = 8(z + 1) Combine like terms: 15z + -4z = 11z -39 + 11z = 8(z + 1) Reorder the terms: -39 + 11z = 8(1 + z) -39 + 11z = (1 * 8 + z * 8) -39 + 11z = (8 + 8z) Solving -39 + 11z = 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. -39 + 11z + -8z = 8 + 8z + -8z Combine like terms: 11z + -8z = 3z -39 + 3z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -39 + 3z = 8 + 0 -39 + 3z = 8 Add '39' to each side of the equation. -39 + 39 + 3z = 8 + 39 Combine like terms: -39 + 39 = 0 0 + 3z = 8 + 39 3z = 8 + 39 Combine like terms: 8 + 39 = 47 3z = 47 Divide each side by '3'. z = 15.66666667 Simplifying z = 15.66666667
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