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Simplifying 3(6z + -1) + -2(z + 4) = 8(z + 1) Reorder the terms: 3(-1 + 6z) + -2(z + 4) = 8(z + 1) (-1 * 3 + 6z * 3) + -2(z + 4) = 8(z + 1) (-3 + 18z) + -2(z + 4) = 8(z + 1) Reorder the terms: -3 + 18z + -2(4 + z) = 8(z + 1) -3 + 18z + (4 * -2 + z * -2) = 8(z + 1) -3 + 18z + (-8 + -2z) = 8(z + 1) Reorder the terms: -3 + -8 + 18z + -2z = 8(z + 1) Combine like terms: -3 + -8 = -11 -11 + 18z + -2z = 8(z + 1) Combine like terms: 18z + -2z = 16z -11 + 16z = 8(z + 1) Reorder the terms: -11 + 16z = 8(1 + z) -11 + 16z = (1 * 8 + z * 8) -11 + 16z = (8 + 8z) Solving -11 + 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. -11 + 16z + -8z = 8 + 8z + -8z Combine like terms: 16z + -8z = 8z -11 + 8z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -11 + 8z = 8 + 0 -11 + 8z = 8 Add '11' to each side of the equation. -11 + 11 + 8z = 8 + 11 Combine like terms: -11 + 11 = 0 0 + 8z = 8 + 11 8z = 8 + 11 Combine like terms: 8 + 11 = 19 8z = 19 Divide each side by '8'. z = 2.375 Simplifying z = 2.375
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