Answer:
-3 < x < 1
Explanation:
In general, an absolute value function is a piecewise-defined function, with each piece having its own applicable domain. However, the absolute value inequality |a| < b is fully equivalent to the compound inequality -b < a < b. This can be used to solve the given inequality.
Isolate the absolute value expression
We can isolate the absolute value expression by undoing the operations done to it.
3|x +1| -2 < 4 . . . . . given
3|x +1| < 6 . . . . . . . add 2
|x +1| < 2 . . . . . . . . divide by 3
Rewrite as a compound inequality and solve
The absolute value inequality is now in the form described above, so can be "unfolded" to a compound inequality:
-2 < x +1 < 2
Subtracting 1 finds the solution for x:
-3 < x < 1