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Simplifying 5(6z + -1) + -3(z + 5) = 24(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 5) = 24(z + 1) (-1 * 5 + 6z * 5) + -3(z + 5) = 24(z + 1) (-5 + 30z) + -3(z + 5) = 24(z + 1) Reorder the terms: -5 + 30z + -3(5 + z) = 24(z + 1) -5 + 30z + (5 * -3 + z * -3) = 24(z + 1) -5 + 30z + (-15 + -3z) = 24(z + 1) Reorder the terms: -5 + -15 + 30z + -3z = 24(z + 1) Combine like terms: -5 + -15 = -20 -20 + 30z + -3z = 24(z + 1) Combine like terms: 30z + -3z = 27z -20 + 27z = 24(z + 1) Reorder the terms: -20 + 27z = 24(1 + z) -20 + 27z = (1 * 24 + z * 24) -20 + 27z = (24 + 24z) Solving -20 + 27z = 24 + 24z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-24z' to each side of the equation. -20 + 27z + -24z = 24 + 24z + -24z Combine like terms: 27z + -24z = 3z -20 + 3z = 24 + 24z + -24z Combine like terms: 24z + -24z = 0 -20 + 3z = 24 + 0 -20 + 3z = 24 Add '20' to each side of the equation. -20 + 20 + 3z = 24 + 20 Combine like terms: -20 + 20 = 0 0 + 3z = 24 + 20 3z = 24 + 20 Combine like terms: 24 + 20 = 44 3z = 44 Divide each side by '3'. z = 14.66666667 Simplifying z = 14.66666667
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