Question

Solve 3|x + 1| –2 < 4

Answer 1

We can start solving the inequality by isolating the absolute value term:

3|x + 1| - 2 < 4

3|x + 1| < 6

|x + 1| < 2

Next, we can split the inequality into two cases, depending on whether the expression inside the absolute value is positive or negative:

x + 1 < 2 or -(x + 1) < 2

Solving for x in each case:

x < 1 or -x - 1 < 2

x < 1 or -x < 3

x < 1 or x > -3

Therefore, the solution to the inequality is the set of all x that satisfy either x < 1 or x > -3, which can be written as:

(-∞, -3) U (1, ∞)

give thanks, your welcome <3

Explanation: