- Thread starter soulmate1
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\(\displaystyle \L\left| {0.6x - 3} \right| > 0.6\quad \Leftrightarrow \quad \left| {x - 5} \right| > 1\).

Now solve these two inequalities:

\(\displaystyle \L x - 5 > 1\quad \text{or}\quad x - 5 < - 1\).

You would draw your number line:

Code:

```
<--|--------|---------|-->
-2 0 2
```

Code:

```
o------>
<--|--------|--------|-->
-2 0 2
```

Then we add the less than -2:

Code:

```
<-------o o-------->
<--|------|------|-->
-2 0 2
```

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- 9,784

One very important thing to observe, when solving, graphing, manipulating, or just playing around, is how to make your life easier. This is what pka showed you. It was a massive step toward just what you are asking. If you see it as only a clue in the wrong direction, this conversation is not going to go well untill you upgrade some other skills.

The "rule" is to proceed in a rational and logical fashion.

In this case, there is simplicity.

Simply

1) Solve 0.6x - 3 = 0.6

2) Check which side of the solution "works".

3) Decide if you should included the end point.

If you are asked to solve a system of inequalities where x>2jonboy said:...Say I have the solution set: x > 2 or x < -2.

(BTW there's no solution to this problem. You can't have a number greater than 2 and less than -2.)

Repeat the above three steps for 3 - 0.6x = 0.6tkhunny said:1) Solve 0.6x - 3 = 0.6

2) Check which side of the solution "works".

3) Decide if you should include the end point.

You are right. Good catch and sorry for any confusion.sean39 said:If you are asked to solve a system of inequalities where x>2andx<2, then it is true that there is no solution. In this case there is a solution by definition since you gave the solution set. The original problem that was posted heredoeshave a solution set which is the union of the two disjoint sets that result from solving the inequality as described by pka.