Question

Solve 3|x + 1| –2 < 4.

Answer 1

Answer:

  -3 < x < 1

Step-by-step 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