Solving inequality | x + 3 | + | 2x-1 | ≥ 7

Solving inequality | x + 3 | + | 2x-1 | ≥ 7

According to the meaning of the question, the discussion of X is divided into three cases: ① when x ≥ 12, the original inequality can be changed into x + 3 + 2x-1 ≥ 7, and the solution is x ≥ 53; ② when - 3 ≤ x < 12, the original inequality can be changed into x + 3 + 1-2x ≥ 7, and the solution is x ≤ - 3, so x = - 3; ③ when x < 3 & nbsp;, the original inequality can be changed into - x-3 + 1-2x ≥ 7, and the solution is x < 3. In conclusion, the solution set of the original inequality is (- ∞, - 3] ∪ [53, +)