Solve the first inequality, 2x+5 1.

Subtract 5 from both sides:

$$2x \ge 1 - 5$$ $$2x \ge -4$$

Divide by 2:

$$x \ge \frac{-4}{2}$$ $$x \ge -2$$

Multiply both sides by 3:

$$x+6 < 4 \times 3$$ $$x+6 < 12$$

Subtract 6 from both sides:

$$x < 12 - 6$$ $$x < 6$$

For $x$ to satisfy both inequalities, it must be greater than or equal to $-2$ AND less than 6.
This can be written as:

$$-2 \le x < 6$$

In interval notation, this is:

$$[-2, 6)$$