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Simplifying 3(4z + -1) + -2(z + 1) = 6(z + 1) Reorder the terms: 3(-1 + 4z) + -2(z + 1) = 6(z + 1) (-1 * 3 + 4z * 3) + -2(z + 1) = 6(z + 1) (-3 + 12z) + -2(z + 1) = 6(z + 1) Reorder the terms: -3 + 12z + -2(1 + z) = 6(z + 1) -3 + 12z + (1 * -2 + z * -2) = 6(z + 1) -3 + 12z + (-2 + -2z) = 6(z + 1) Reorder the terms: -3 + -2 + 12z + -2z = 6(z + 1) Combine like terms: -3 + -2 = -5 -5 + 12z + -2z = 6(z + 1) Combine like terms: 12z + -2z = 10z -5 + 10z = 6(z + 1) Reorder the terms: -5 + 10z = 6(1 + z) -5 + 10z = (1 * 6 + z * 6) -5 + 10z = (6 + 6z) Solving -5 + 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. -5 + 10z + -6z = 6 + 6z + -6z Combine like terms: 10z + -6z = 4z -5 + 4z = 6 + 6z + -6z Combine like terms: 6z + -6z = 0 -5 + 4z = 6 + 0 -5 + 4z = 6 Add '5' to each side of the equation. -5 + 5 + 4z = 6 + 5 Combine like terms: -5 + 5 = 0 0 + 4z = 6 + 5 4z = 6 + 5 Combine like terms: 6 + 5 = 11 4z = 11 Divide each side by '4'. z = 2.75 Simplifying z = 2.75
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