Question

What is the solution set of 1=<|x+3|<=4?

Answer 1

The solution set of the inequality 1 <= |x+3| <= 4 is -4 <= x <= -2 or 1 <= x <= 4.

Step-by-step explanation:

The solution set of the inequality 1 <= |x+3| <= 4 can be found by considering two cases: when x+3 is positive and when x+3 is negative.

Case 1: x+3 > 0

1. When x+3 > 0, the inequality becomes 1 <= x+3 <= 4.
2. By subtracting 3 from all parts of the inequality, we get -2 <= x <= 1.

Case 2: x+3 < 0

1. When x+3 < 0, the inequality becomes 1 <= -x-3 <= 4.
2. By adding 3 to all parts of the inequality and multiplying by -1, we get -4 <= -x <= -1.
3. Dividing all parts of the inequality by -1, we get 1 <= x <= 4.

Combining the solutions from both cases, the solution set is -4 <= x <= -2 or 1 <= x <= 4.