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Simplifying 3(5z + -1) + -5(z + 6) = 4(z + 1) Reorder the terms: 3(-1 + 5z) + -5(z + 6) = 4(z + 1) (-1 * 3 + 5z * 3) + -5(z + 6) = 4(z + 1) (-3 + 15z) + -5(z + 6) = 4(z + 1) Reorder the terms: -3 + 15z + -5(6 + z) = 4(z + 1) -3 + 15z + (6 * -5 + z * -5) = 4(z + 1) -3 + 15z + (-30 + -5z) = 4(z + 1) Reorder the terms: -3 + -30 + 15z + -5z = 4(z + 1) Combine like terms: -3 + -30 = -33 -33 + 15z + -5z = 4(z + 1) Combine like terms: 15z + -5z = 10z -33 + 10z = 4(z + 1) Reorder the terms: -33 + 10z = 4(1 + z) -33 + 10z = (1 * 4 + z * 4) -33 + 10z = (4 + 4z) Solving -33 + 10z = 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. -33 + 10z + -4z = 4 + 4z + -4z Combine like terms: 10z + -4z = 6z -33 + 6z = 4 + 4z + -4z Combine like terms: 4z + -4z = 0 -33 + 6z = 4 + 0 -33 + 6z = 4 Add '33' to each side of the equation. -33 + 33 + 6z = 4 + 33 Combine like terms: -33 + 33 = 0 0 + 6z = 4 + 33 6z = 4 + 33 Combine like terms: 4 + 33 = 37 6z = 37 Divide each side by '6'. z = 6.166666667 Simplifying z = 6.166666667
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