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Simplifying 3z + 2[2 + 3(z + -1)] = 2(3z + 4) Reorder the terms: 3z + 2[2 + 3(-1 + z)] = 2(3z + 4) 3z + 2[2 + (-1 * 3 + z * 3)] = 2(3z + 4) 3z + 2[2 + (-3 + 3z)] = 2(3z + 4) Combine like terms: 2 + -3 = -1 3z + 2[-1 + 3z] = 2(3z + 4) 3z + [-1 * 2 + 3z * 2] = 2(3z + 4) 3z + [-2 + 6z] = 2(3z + 4) Reorder the terms: -2 + 3z + 6z = 2(3z + 4) Combine like terms: 3z + 6z = 9z -2 + 9z = 2(3z + 4) Reorder the terms: -2 + 9z = 2(4 + 3z) -2 + 9z = (4 * 2 + 3z * 2) -2 + 9z = (8 + 6z) Solving -2 + 9z = 8 + 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. -2 + 9z + -6z = 8 + 6z + -6z Combine like terms: 9z + -6z = 3z -2 + 3z = 8 + 6z + -6z Combine like terms: 6z + -6z = 0 -2 + 3z = 8 + 0 -2 + 3z = 8 Add '2' to each side of the equation. -2 + 2 + 3z = 8 + 2 Combine like terms: -2 + 2 = 0 0 + 3z = 8 + 2 3z = 8 + 2 Combine like terms: 8 + 2 = 10 3z = 10 Divide each side by '3'. z = 3.333333333 Simplifying z = 3.333333333
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