Solve |x + 3| > 2 Step by Step | Absolute value inequalities

Step by step

The question

Question: solve |x + 3| > 2.

|x + 3| > 2

1 Draw the distance

2 Write it without bars

So x + 3 < −2 or x + 3 > 2.

x + 3 < −2 or x + 3 > 2

"Or" means: x can make one of them true, or the other.

We solve both, side by side.

or: one of them is true

3 Remove the + 3

We want x by itself.

The + 3 is in the way.

In each one, we take away 3 on both sides.

x ~~+ 3 − 3~~ < −2 − 3 or x ~~+ 3 − 3~~ > 2 − 3

+ 3 and − 3 make zero, in both.

−2 minus 3 is −5.

2 minus 3 is −1.

−2 − 3 = −5, 2 − 3 = −1

So x < −5 or x > −1.

x < −5 or x > −1

4 Show it on a number line

Books also write the answer like this.

It is called interval notation.

A round bracket means the end is not in, like the open circle.

∞ means it goes on for ever.

∪ means or.

interval: (−∞, −5) ∪ (−1, ∞)

5 Check

Let's test one number from each part, in the question.

First −6.

x = −6: |−6 + 3| = |−3| = 3

3 is greater than 2.

True!

3 > 2

Now 1, from the right part.

x = 1: |1 + 3| = |4| = 4

4 is greater than 2.

True!

Both parts work!

4 > 2

Let's look back.

First: draw the distance.

Then: write it without bars.

Then: remove the + 3.

Then: show it on a number line.

Last: check.

Answer