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.