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Simplifying 11(z + 3) + -4(z + -2) = 2(z + -2) + 4(z + -1) Reorder the terms: 11(3 + z) + -4(z + -2) = 2(z + -2) + 4(z + -1) (3 * 11 + z * 11) + -4(z + -2) = 2(z + -2) + 4(z + -1) (33 + 11z) + -4(z + -2) = 2(z + -2) + 4(z + -1) Reorder the terms: 33 + 11z + -4(-2 + z) = 2(z + -2) + 4(z + -1) 33 + 11z + (-2 * -4 + z * -4) = 2(z + -2) + 4(z + -1) 33 + 11z + (8 + -4z) = 2(z + -2) + 4(z + -1) Reorder the terms: 33 + 8 + 11z + -4z = 2(z + -2) + 4(z + -1) Combine like terms: 33 + 8 = 41 41 + 11z + -4z = 2(z + -2) + 4(z + -1) Combine like terms: 11z + -4z = 7z 41 + 7z = 2(z + -2) + 4(z + -1) Reorder the terms: 41 + 7z = 2(-2 + z) + 4(z + -1) 41 + 7z = (-2 * 2 + z * 2) + 4(z + -1) 41 + 7z = (-4 + 2z) + 4(z + -1) Reorder the terms: 41 + 7z = -4 + 2z + 4(-1 + z) 41 + 7z = -4 + 2z + (-1 * 4 + z * 4) 41 + 7z = -4 + 2z + (-4 + 4z) Reorder the terms: 41 + 7z = -4 + -4 + 2z + 4z Combine like terms: -4 + -4 = -8 41 + 7z = -8 + 2z + 4z Combine like terms: 2z + 4z = 6z 41 + 7z = -8 + 6z Solving 41 + 7z = -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. 41 + 7z + -6z = -8 + 6z + -6z Combine like terms: 7z + -6z = 1z 41 + 1z = -8 + 6z + -6z Combine like terms: 6z + -6z = 0 41 + 1z = -8 + 0 41 + 1z = -8 Add '-41' to each side of the equation. 41 + -41 + 1z = -8 + -41 Combine like terms: 41 + -41 = 0 0 + 1z = -8 + -41 1z = -8 + -41 Combine like terms: -8 + -41 = -49 1z = -49 Divide each side by '1'. z = -49 Simplifying z = -49
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