Find the solution set for the system of linear inequalities: 3x - 7 < 5 + x and 11 - 5x ≤ 1.

Model Answer & Options

Source: Extra Practice

[2, 6)

(2, 6]

[2, 6]

(2, 6)

Explanation

Solve each inequality separately. For the first: 3x - 7 3x - x 2x x 11 - 1 ≤ 5x => 10 ≤ 5x => 2 ≤ x. This means x must be greater than or equal to 2 AND strictly less than 6. Combining these, we get 2 ≤ x < 6. In interval notation, this is written as [2, 6). Option B reverses the inclusion of endpoints. Option C incorrectly includes 6. Option D incorrectly excludes 2.

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