∣x+10∣<2
To solve the inequality ∣x + 10∣ < 2, we can consider two cases:
Case 1: x + 10 is positive
If x + 10 > 0, then the inequality becomes x + 10 < 2.
Solving this inequality, we have x < -8.
Case 2: x + 10 is negative
If x + 10 < 0, we can rewrite the inequality as -(x + 10) < 2.
This simplifies to -x - 10 < 2, which can be further reduced to -x < 12.
Multiplying both sides by -1, we get x > -12.
Therefore, the solution to the inequality ∣x + 10∣ < 2 is -12 < x < -8.