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Simplifying 2[3 + -2(z + 4)] = 3(4 + z) Reorder the terms: 2[3 + -2(4 + z)] = 3(4 + z) 2[3 + (4 * -2 + z * -2)] = 3(4 + z) 2[3 + (-8 + -2z)] = 3(4 + z) Combine like terms: 3 + -8 = -5 2[-5 + -2z] = 3(4 + z) [-5 * 2 + -2z * 2] = 3(4 + z) [-10 + -4z] = 3(4 + z) -10 + -4z = (4 * 3 + z * 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 = -7z -10 + -7z = 12 + 3z + -3z Combine like terms: 3z + -3z = 0 -10 + -7z = 12 + 0 -10 + -7z = 12 Add '10' to each side of the equation. -10 + 10 + -7z = 12 + 10 Combine like terms: -10 + 10 = 0 0 + -7z = 12 + 10 -7z = 12 + 10 Combine like terms: 12 + 10 = 22 -7z = 22 Divide each side by '-7'. z = -3.142857143 Simplifying z = -3.142857143
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