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Simplifying 5(6z + -1) + -3(z + 1) = 21(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 1) = 21(z + 1) (-1 * 5 + 6z * 5) + -3(z + 1) = 21(z + 1) (-5 + 30z) + -3(z + 1) = 21(z + 1) Reorder the terms: -5 + 30z + -3(1 + z) = 21(z + 1) -5 + 30z + (1 * -3 + z * -3) = 21(z + 1) -5 + 30z + (-3 + -3z) = 21(z + 1) Reorder the terms: -5 + -3 + 30z + -3z = 21(z + 1) Combine like terms: -5 + -3 = -8 -8 + 30z + -3z = 21(z + 1) Combine like terms: 30z + -3z = 27z -8 + 27z = 21(z + 1) Reorder the terms: -8 + 27z = 21(1 + z) -8 + 27z = (1 * 21 + z * 21) -8 + 27z = (21 + 21z) Solving -8 + 27z = 21 + 21z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-21z' to each side of the equation. -8 + 27z + -21z = 21 + 21z + -21z Combine like terms: 27z + -21z = 6z -8 + 6z = 21 + 21z + -21z Combine like terms: 21z + -21z = 0 -8 + 6z = 21 + 0 -8 + 6z = 21 Add '8' to each side of the equation. -8 + 8 + 6z = 21 + 8 Combine like terms: -8 + 8 = 0 0 + 6z = 21 + 8 6z = 21 + 8 Combine like terms: 21 + 8 = 29 6z = 29 Divide each side by '6'. z = 4.833333333 Simplifying z = 4.833333333
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