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Simplifying 3(6z + -1) + -4(z + 5) = 8(z + 1) Reorder the terms: 3(-1 + 6z) + -4(z + 5) = 8(z + 1) (-1 * 3 + 6z * 3) + -4(z + 5) = 8(z + 1) (-3 + 18z) + -4(z + 5) = 8(z + 1) Reorder the terms: -3 + 18z + -4(5 + z) = 8(z + 1) -3 + 18z + (5 * -4 + z * -4) = 8(z + 1) -3 + 18z + (-20 + -4z) = 8(z + 1) Reorder the terms: -3 + -20 + 18z + -4z = 8(z + 1) Combine like terms: -3 + -20 = -23 -23 + 18z + -4z = 8(z + 1) Combine like terms: 18z + -4z = 14z -23 + 14z = 8(z + 1) Reorder the terms: -23 + 14z = 8(1 + z) -23 + 14z = (1 * 8 + z * 8) -23 + 14z = (8 + 8z) Solving -23 + 14z = 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. -23 + 14z + -8z = 8 + 8z + -8z Combine like terms: 14z + -8z = 6z -23 + 6z = 8 + 8z + -8z Combine like terms: 8z + -8z = 0 -23 + 6z = 8 + 0 -23 + 6z = 8 Add '23' to each side of the equation. -23 + 23 + 6z = 8 + 23 Combine like terms: -23 + 23 = 0 0 + 6z = 8 + 23 6z = 8 + 23 Combine like terms: 8 + 23 = 31 6z = 31 Divide each side by '6'. z = 5.166666667 Simplifying z = 5.166666667
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