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Simplifying 2(6z + -1) + -3(z + 5) = 6(z + 1) Reorder the terms: 2(-1 + 6z) + -3(z + 5) = 6(z + 1) (-1 * 2 + 6z * 2) + -3(z + 5) = 6(z + 1) (-2 + 12z) + -3(z + 5) = 6(z + 1) Reorder the terms: -2 + 12z + -3(5 + z) = 6(z + 1) -2 + 12z + (5 * -3 + z * -3) = 6(z + 1) -2 + 12z + (-15 + -3z) = 6(z + 1) Reorder the terms: -2 + -15 + 12z + -3z = 6(z + 1) Combine like terms: -2 + -15 = -17 -17 + 12z + -3z = 6(z + 1) Combine like terms: 12z + -3z = 9z -17 + 9z = 6(z + 1) Reorder the terms: -17 + 9z = 6(1 + z) -17 + 9z = (1 * 6 + z * 6) -17 + 9z = (6 + 6z) Solving -17 + 9z = 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. -17 + 9z + -6z = 6 + 6z + -6z Combine like terms: 9z + -6z = 3z -17 + 3z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -17 + 3z = 6 + 0 -17 + 3z = 6 Add '17' to each side of the equation. -17 + 17 + 3z = 6 + 17 Combine like terms: -17 + 17 = 0 0 + 3z = 6 + 17 3z = 6 + 17 Combine like terms: 6 + 17 = 23 3z = 23 Divide each side by '3'. z = 7.666666667 Simplifying z = 7.666666667
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