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Simplifying 5(6z + -1) + -3(z + 1) = 4(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 1) = 4(z + 1) (-1 * 5 + 6z * 5) + -3(z + 1) = 4(z + 1) (-5 + 30z) + -3(z + 1) = 4(z + 1) Reorder the terms: -5 + 30z + -3(1 + z) = 4(z + 1) -5 + 30z + (1 * -3 + z * -3) = 4(z + 1) -5 + 30z + (-3 + -3z) = 4(z + 1) Reorder the terms: -5 + -3 + 30z + -3z = 4(z + 1) Combine like terms: -5 + -3 = -8 -8 + 30z + -3z = 4(z + 1) Combine like terms: 30z + -3z = 27z -8 + 27z = 4(z + 1) Reorder the terms: -8 + 27z = 4(1 + z) -8 + 27z = (1 * 4 + z * 4) -8 + 27z = (4 + 4z) Solving -8 + 27z = 4 + 4z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4z' to each side of the equation. -8 + 27z + -4z = 4 + 4z + -4z Combine like terms: 27z + -4z = 23z -8 + 23z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -8 + 23z = 4 + 0 -8 + 23z = 4 Add '8' to each side of the equation. -8 + 8 + 23z = 4 + 8 Combine like terms: -8 + 8 = 0 0 + 23z = 4 + 8 23z = 4 + 8 Combine like terms: 4 + 8 = 12 23z = 12 Divide each side by '23'. z = 0.5217391304 Simplifying z = 0.5217391304
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