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Simplifying 5(3z + -1) + -5(z + 2) = 6(z + 1) Reorder the terms: 5(-1 + 3z) + -5(z + 2) = 6(z + 1) (-1 * 5 + 3z * 5) + -5(z + 2) = 6(z + 1) (-5 + 15z) + -5(z + 2) = 6(z + 1) Reorder the terms: -5 + 15z + -5(2 + z) = 6(z + 1) -5 + 15z + (2 * -5 + z * -5) = 6(z + 1) -5 + 15z + (-10 + -5z) = 6(z + 1) Reorder the terms: -5 + -10 + 15z + -5z = 6(z + 1) Combine like terms: -5 + -10 = -15 -15 + 15z + -5z = 6(z + 1) Combine like terms: 15z + -5z = 10z -15 + 10z = 6(z + 1) Reorder the terms: -15 + 10z = 6(1 + z) -15 + 10z = (1 * 6 + z * 6) -15 + 10z = (6 + 6z) Solving -15 + 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. -15 + 10z + -6z = 6 + 6z + -6z Combine like terms: 10z + -6z = 4z -15 + 4z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -15 + 4z = 6 + 0 -15 + 4z = 6 Add '15' to each side of the equation. -15 + 15 + 4z = 6 + 15 Combine like terms: -15 + 15 = 0 0 + 4z = 6 + 15 4z = 6 + 15 Combine like terms: 6 + 15 = 21 4z = 21 Divide each side by '4'. z = 5.25 Simplifying z = 5.25
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