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Simplifying 5(3z + -1) + -5(z + 4) = 6(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 4) = 6(z + 1) (-1 * 5 + 3z * 5) + -5(z + 4) = 6(z + 1) (-5 + 15z) + -5(z + 4) = 6(z + 1) Reorder the terms: -5 + 15z + -5(4 + z) = 6(z + 1) -5 + 15z + (4 * -5 + z * -5) = 6(z + 1) -5 + 15z + (-20 + -5z) = 6(z + 1) Reorder the terms: -5 + -20 + 15z + -5z = 6(z + 1) Combine like terms: -5 + -20 = -25 -25 + 15z + -5z = 6(z + 1) Combine like terms: 15z + -5z = 10z -25 + 10z = 6(z + 1) Reorder the terms: -25 + 10z = 6(1 + z) -25 + 10z = (1 * 6 + z * 6) -25 + 10z = (6 + 6z) Solving -25 + 10z = 6 + 6z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-6z' to each side of the equation. -25 + 10z + -6z = 6 + 6z + -6z Combine like terms: 10z + -6z = 4z -25 + 4z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -25 + 4z = 6 + 0 -25 + 4z = 6 Add '25' to each side of the equation. -25 + 25 + 4z = 6 + 25 Combine like terms: -25 + 25 = 0 0 + 4z = 6 + 25 4z = 6 + 25 Combine like terms: 6 + 25 = 31 4z = 31 Divide each side by '4'. z = 7.75 Simplifying z = 7.75
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