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Simplifying -4z + 2(z + 1) + 3(z + -2) = 7 Reorder the terms: -4z + 2(1 + z) + 3(z + -2) = 7 -4z + (1 * 2 + z * 2) + 3(z + -2) = 7 -4z + (2 + 2z) + 3(z + -2) = 7 Reorder the terms: -4z + 2 + 2z + 3(-2 + z) = 7 -4z + 2 + 2z + (-2 * 3 + z * 3) = 7 -4z + 2 + 2z + (-6 + 3z) = 7 Reorder the terms: 2 + -6 + -4z + 2z + 3z = 7 Combine like terms: 2 + -6 = -4 -4 + -4z + 2z + 3z = 7 Combine like terms: -4z + 2z = -2z -4 + -2z + 3z = 7 Combine like terms: -2z + 3z = 1z -4 + 1z = 7 Solving -4 + 1z = 7 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 1z = 7 + 4 Combine like terms: -4 + 4 = 0 0 + 1z = 7 + 4 1z = 7 + 4 Combine like terms: 7 + 4 = 11 1z = 11 Divide each side by '1'. z = 11 Simplifying z = 11
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