Answer:
-3 < x < 1
Explanation:
To solve the inequality 3|x+1| < 6, we need to isolate the absolute value expression and solve for the variable x. We can start by dividing both sides of the inequality by 3:
|x+1| < 2
Next, we can split the inequality into two separate cases, one for when x+1 is positive and one for when x+1 is negative. When x+1 is positive, we can remove the absolute value bars, so we have:
x+1 < 2
Solving for x, we get:
x < 1
When x+1 is negative, we need to distribute the negative sign that comes with the absolute value expression, so we have:
-(x+1) < 2
Multiplying both sides by -1 (which reverses the direction of the inequality), we have:
x+1 > -2
Subtracting 1 from both sides, we get:
x > -3
So the solution to the inequality is:
-3 < x < 1