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Simplifying 5(6z + -1) + -3(z + 7) = 6(z + 1) Reorder the terms: 5(-1 + 6z) + -3(z + 7) = 6(z + 1) (-1 * 5 + 6z * 5) + -3(z + 7) = 6(z + 1) (-5 + 30z) + -3(z + 7) = 6(z + 1) Reorder the terms: -5 + 30z + -3(7 + z) = 6(z + 1) -5 + 30z + (7 * -3 + z * -3) = 6(z + 1) -5 + 30z + (-21 + -3z) = 6(z + 1) Reorder the terms: -5 + -21 + 30z + -3z = 6(z + 1) Combine like terms: -5 + -21 = -26 -26 + 30z + -3z = 6(z + 1) Combine like terms: 30z + -3z = 27z -26 + 27z = 6(z + 1) Reorder the terms: -26 + 27z = 6(1 + z) -26 + 27z = (1 * 6 + z * 6) -26 + 27z = (6 + 6z) Solving -26 + 27z = 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. -26 + 27z + -6z = 6 + 6z + -6z Combine like terms: 27z + -6z = 21z -26 + 21z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -26 + 21z = 6 + 0 -26 + 21z = 6 Add '26' to each side of the equation. -26 + 26 + 21z = 6 + 26 Combine like terms: -26 + 26 = 0 0 + 21z = 6 + 26 21z = 6 + 26 Combine like terms: 6 + 26 = 32 21z = 32 Divide each side by '21'. z = 1.523809524 Simplifying z = 1.523809524
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