Solving inequalities: -3 < 2x-1/ 4 < 0 and 1 < 1 - 1/2x < 4

[weaver32]

1. -3 < 2x-1/ 4 < 0

and

2. 1 < 1 - 1/2x < 4

 

[Deleted member 4993]

Re: Solving inequalities

1. -3 < 2x-1/ 4 < 0

and

2. 1 < 1 - 1/2x < 4

for a quick review go to:

http://www.purplemath.com/modules/ineqsolv.htm

 

[kasie-tutor]

Re: Solving inequalities

Think of these problems as three-sided equations. i.e., (left-side)<(middle)<(right-side). The goal is to isolate x. What you do to one side of the equation, you must do to the other two sides.

There is a possible pitfall in inequalities having to do with multiplying or dividing by a negative. Graph your answer on a number line.

I think your very best source for examples may be your textbook, if you have it with you.



Kasie

 

[stapel]

1. -3 < 2x-1/ 4 < 0

and

2. 1 < 1 - 1/2x < 4

These can usually be split into two separate problems, each with only one inequality symbol. However, I'm not clear on quite what the inequalities are...?

For (1), you might mean this:

. . . . .\(\displaystyle -3\, <\, \frac{2x\, -\, 1}{4}\, < \, 0\)

...or this:

. . . . .\(\displaystyle -3\, <\, 2x\, -\, \frac{1}{4}\, <\, 0\)

...or something else. For (2), you might mean this:

. . . . .\(\displaystyle 1\, <\, 1\, -\, \frac{1}{2x}\, <\, 4\)

...or this:

. . . . .\(\displaystyle 1\, <\, 1\, -\, \frac{1}{2}x\, <\, 4\)

...or something else. The method of solution will vary with your meaning, so please reply with clarification. When you reply, please include a clear listing of everything you have tried so far. Thank you!

Eliz.