Question

Solve the inequity for x and identify the graph of its solution.|x+2|<2

Answer 1

Given:

|x + 2| < 2

Let's solve for x.

Given the absolute value, we have 2 conditions. They are:

x + 2 < 2 and x + 2 > -2

Let's find x for both conditions.

Condition 1:

x + 2 < 2

Subtract 2 from both sides:

x + 2 - 2 < 2 - 2

x < 0

Condition 2:

x + 2 > -2

Subtract 2 from both sides:

x + 2 - 2 > -2 - 2

x > -4

Therefore,

x < 0 and x > -4

In interval notation, we have the solution as:

(-4, 0)

The graph of the inequality is below: