Source: Extra Practice

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

Options

Option A is correct

[2, 6)

Option B

(2, 6]

Option C

[2, 6]

Option D

(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.