Solving Inequality 4x<2x+1(<=)3x+2 in terms of interva

lostislandgirl2 said:
Am i supposed to get all the terms to equal zero?
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I'm sorry, but I don't know what you mean...? :shock:

To learn how to solve linear inequalities, please study some of the many lessons available online:

. . . . .Google results for "solving linear inequalities"

First study how to solve the inequalities with just one "greater than" or "less than" symbol (so the inequality has two parts); then move on to inequalities with two inequality symbols (so the inequalities have three parts). The techniques are the same, but the two-part inequalities, naturally, are easier to work with, and thus easier to learn from. :wink:

Once you have studied some lessons (at least two!), please attempt this exercise. If you get stuck, please reply showing all of your work and reasoning, and we'll be glad to try to help you get un-stuck! :D

Eliz.
 
If there is a solution, it must satisfy both 4x<2x+1 and 2x+1<=3x+2.
 
Thanks! so I went to purplemath and looked at solving inequalities.


And I got where each "side" (each of the 3 terms) has to have the same operation completed...for instance: If I want to subtract 2x from each term in the inequality 4x<2x+1<,=3x+2, I get: 2x<1 <= x...at this point, do I solve for each x term? 2x<1 x=1/2 and 1<=x, x=-1?
 
lostislandgirl2 said:
If I want to subtract 2x from each term in the inequality 4x<2x+1<,=3x+2, I get: 2x<1 <= x...at this point, do I solve for each x term? 2x<1 x=1/2 and 1<=x, x=-1?
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I'm not sure what you did here...? (Writing out steps on individual lines, with reasoning between, can be very helpful, by the way.)

You have the following inequality:

. . . . .4x < 2x + 1 < 3x + 2

As a previous tutor explained, you're wanting to solve two inequalities from this:

. . . . .4x < 2x + 1

. . . . .2x + 1 < 3x + 2

Subtracting 2x from either side of each is one way to go:

. . . . .2x < 1

. . . . .1 < x + 2

For the first, the solution requires dividing through by 2. For the second, subtract 2 from either side. :D

Note: You should end up with inequalities. You should not have "equals" signs when you're done! :shock:

Eliz.
 
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