Outside, Shifted

In $\left|2x+1\right| \ge 5$, the expression inside the bars is $2x+1$. Split into the two cases, then solve each case as a two-step inequality.

$$2x+1 \ge 5$$

$$2x \ge 4$$

$$x \ge 2$$

or

$$2x+1 \le -5$$

$$2x \le -6$$

$$x \le -3$$

The solution is $x \le -3$ or $x \ge 2$. On a number line, these are two rays pointing away from each other.

Solve each case with the ordinary inequality rules. If a case has a negative coefficient, flip the sign when you divide, as usual. Keep both cases to the end, and keep the word "or" between the two answers.