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Simplifying 2[3 + -2(z + 4)] = 3(4 + -1z) Reorder the terms: 2[3 + -2(4 + z)] = 3(4 + -1z) 2[3 + (4 * -2 + z * -2)] = 3(4 + -1z) 2[3 + (-8 + -2z)] = 3(4 + -1z) Combine like terms: 3 + -8 = -5 2[-5 + -2z] = 3(4 + -1z) [-5 * 2 + -2z * 2] = 3(4 + -1z) [-10 + -4z] = 3(4 + -1z) -10 + -4z = (4 * 3 + -1z * 3) -10 + -4z = (12 + -3z) Solving -10 + -4z = 12 + -3z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '3z' to each side of the equation. -10 + -4z + 3z = 12 + -3z + 3z Combine like terms: -4z + 3z = -1z -10 + -1z = 12 + -3z + 3z Combine like terms: -3z + 3z = 0 -10 + -1z = 12 + 0 -10 + -1z = 12 Add '10' to each side of the equation. -10 + 10 + -1z = 12 + 10 Combine like terms: -10 + 10 = 0 0 + -1z = 12 + 10 -1z = 12 + 10 Combine like terms: 12 + 10 = 22 -1z = 22 Divide each side by '-1'. z = -22 Simplifying z = -22
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