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Simplifying -2 + -6z + 3 = 4 + -1[6 + -1z + -1(3 + -2z)] Reorder the terms: -2 + 3 + -6z = 4 + -1[6 + -1z + -1(3 + -2z)] Combine like terms: -2 + 3 = 1 1 + -6z = 4 + -1[6 + -1z + -1(3 + -2z)] 1 + -6z = 4 + -1[6 + -1z + (3 * -1 + -2z * -1)] 1 + -6z = 4 + -1[6 + -1z + (-3 + 2z)] Reorder the terms: 1 + -6z = 4 + -1[6 + -3 + -1z + 2z] Combine like terms: 6 + -3 = 3 1 + -6z = 4 + -1[3 + -1z + 2z] Combine like terms: -1z + 2z = 1z 1 + -6z = 4 + -1[3 + 1z] 1 + -6z = 4 + [3 * -1 + 1z * -1] 1 + -6z = 4 + [-3 + -1z] Combine like terms: 4 + -3 = 1 1 + -6z = 1 + -1z Add '-1' to each side of the equation. 1 + -1 + -6z = 1 + -1 + -1z Combine like terms: 1 + -1 = 0 0 + -6z = 1 + -1 + -1z -6z = 1 + -1 + -1z Combine like terms: 1 + -1 = 0 -6z = 0 + -1z -6z = -1z Solving -6z = -1z Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add 'z' to each side of the equation. -6z + z = -1z + z Combine like terms: -6z + z = -5z -5z = -1z + z Combine like terms: -1z + z = 0 -5z = 0 Divide each side by '-5'. z = 0 Simplifying z = 0
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