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Simplifying 5(6z + -1) + -3(z + 9) = 21(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 9) = 21(z + 1) (-1 * 5 + 6z * 5) + -3(z + 9) = 21(z + 1) (-5 + 30z) + -3(z + 9) = 21(z + 1) Reorder the terms: -5 + 30z + -3(9 + z) = 21(z + 1) -5 + 30z + (9 * -3 + z * -3) = 21(z + 1) -5 + 30z + (-27 + -3z) = 21(z + 1) Reorder the terms: -5 + -27 + 30z + -3z = 21(z + 1) Combine like terms: -5 + -27 = -32 -32 + 30z + -3z = 21(z + 1) Combine like terms: 30z + -3z = 27z -32 + 27z = 21(z + 1) Reorder the terms: -32 + 27z = 21(1 + z) -32 + 27z = (1 * 21 + z * 21) -32 + 27z = (21 + 21z) Solving -32 + 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. -32 + 27z + -21z = 21 + 21z + -21z Combine like terms: 27z + -21z = 6z -32 + 6z = 21 + 21z + -21z Combine like terms: 21z + -21z = 0 -32 + 6z = 21 + 0 -32 + 6z = 21 Add '32' to each side of the equation. -32 + 32 + 6z = 21 + 32 Combine like terms: -32 + 32 = 0 0 + 6z = 21 + 32 6z = 21 + 32 Combine like terms: 21 + 32 = 53 6z = 53 Divide each side by '6'. z = 8.833333333 Simplifying z = 8.833333333
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