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Simplifying 3(6z + -1) + -2(z + 9) = 8(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 9) = 8(z + 1) (-1 * 3 + 6z * 3) + -2(z + 9) = 8(z + 1) (-3 + 18z) + -2(z + 9) = 8(z + 1) Reorder the terms: -3 + 18z + -2(9 + z) = 8(z + 1) -3 + 18z + (9 * -2 + z * -2) = 8(z + 1) -3 + 18z + (-18 + -2z) = 8(z + 1) Reorder the terms: -3 + -18 + 18z + -2z = 8(z + 1) Combine like terms: -3 + -18 = -21 -21 + 18z + -2z = 8(z + 1) Combine like terms: 18z + -2z = 16z -21 + 16z = 8(z + 1) Reorder the terms: -21 + 16z = 8(1 + z) -21 + 16z = (1 * 8 + z * 8) -21 + 16z = (8 + 8z) Solving -21 + 16z = 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. -21 + 16z + -8z = 8 + 8z + -8z Combine like terms: 16z + -8z = 8z -21 + 8z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -21 + 8z = 8 + 0 -21 + 8z = 8 Add '21' to each side of the equation. -21 + 21 + 8z = 8 + 21 Combine like terms: -21 + 21 = 0 0 + 8z = 8 + 21 8z = 8 + 21 Combine like terms: 8 + 21 = 29 8z = 29 Divide each side by '8'. z = 3.625 Simplifying z = 3.625
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