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Simplifying 5(6z + -1) + -4(z + 7) = 20(z + 1) Reorder the terms: 5(-1 + 6z) + -4(z + 7) = 20(z + 1) (-1 * 5 + 6z * 5) + -4(z + 7) = 20(z + 1) (-5 + 30z) + -4(z + 7) = 20(z + 1) Reorder the terms: -5 + 30z + -4(7 + z) = 20(z + 1) -5 + 30z + (7 * -4 + z * -4) = 20(z + 1) -5 + 30z + (-28 + -4z) = 20(z + 1) Reorder the terms: -5 + -28 + 30z + -4z = 20(z + 1) Combine like terms: -5 + -28 = -33 -33 + 30z + -4z = 20(z + 1) Combine like terms: 30z + -4z = 26z -33 + 26z = 20(z + 1) Reorder the terms: -33 + 26z = 20(1 + z) -33 + 26z = (1 * 20 + z * 20) -33 + 26z = (20 + 20z) Solving -33 + 26z = 20 + 20z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-20z' to each side of the equation. -33 + 26z + -20z = 20 + 20z + -20z Combine like terms: 26z + -20z = 6z -33 + 6z = 20 + 20z + -20z Combine like terms: 20z + -20z = 0 -33 + 6z = 20 + 0 -33 + 6z = 20 Add '33' to each side of the equation. -33 + 33 + 6z = 20 + 33 Combine like terms: -33 + 33 = 0 0 + 6z = 20 + 33 6z = 20 + 33 Combine like terms: 20 + 33 = 53 6z = 53 Divide each side by '6'. z = 8.833333333 Simplifying z = 8.833333333
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