# Solving Inequality: 2x/3 < 3x - 1/2 <= - 1

#### dk_102

##### New member
Solve the inequality:

2x/3 < 3x - 1/2 < - 1

My problem is that I don't know where to begin or what really I'm supposed to be doing. I would appreciate any help!

dom

#### tkhunny

##### Moderator
Staff member
dk_102 said:
Solve the inequality:

2x/3 < 3x - 1/2 < - 1

My problem is that I don't know where to begin or what really I'm supposed to be doing. I would appreciate any help!

dom
$$\displaystyle \L\,\frac{2}{3}x \lt 3x - \frac{1}{2} \le -1$$

One thing some folks like to do is get rid of fractions. Multiply by 6. Why did I pick '6'?

$$\displaystyle \L\,4x \lt 18x - 3 \le -6$$

If there were a convenient 'x' in only one place, this would be fine. As it is not the case, we'll have to break it up.

$$\displaystyle \L\,4x \lt 18x - 3$$
AND
$$\displaystyle \L\,18x - 3 \le -6$$ -- This one simplifies nicely. -- $$\displaystyle \L\,6x - 1 \le -2$$

Can you solve both of those?

Note: It was NOT necessary to clear the fractions. Frankly, we're just going to get them back. It would be good to learn how to deal with them.