Example of rational inequalities, Algebra

Solve (3x+ 1/ x + 4 ) ≥ 1.

Solution

The first thing that we have to do here is subtract 1 from both of sides and then get everything in a single rational expression.

 (3x + 1/ x + 4) -1 ≥ 0

(3x + 1/x+4) - (x + 4/x+4) ≥ 0

 (3x +1 - ( x + 4))/ x + 4  ≥ 0

2 x - 3 / x + 4 ≥ 0

In this case there is no factoring to do thus we can go straight to recognizing where the numerator & denominator are zero.

numerator : x = 3/2                         denominator : x = -4

Following is the number line for this problem.

322_Rational Inequalities.png

Okay, we desire values of x that give positive and/or zero in the rational expression. It looks like the outer two regions as well as x = 3/2        .  As with the first instance we will have to avoid x = -4 since that will give a division by zero error.

Then the solution for this problem is,

-∞ < x < -4    and            3/2 ≤ x < ∞

( -∞, -4)       and         [3 , ∞ )

Posted Date: 4/6/2013 5:33:32 AM | Location : United States







Related Discussions:- Example of rational inequalities, Assignment Help, Ask Question on Example of rational inequalities, Get Answer, Expert's Help, Example of rational inequalities Discussions

Write discussion on Example of rational inequalities
Your posts are moderated
Related Questions

We have to note a couple of things here regarding function composition.  Primary it is NOT multiplication. Regardless of what the notation may recommend to you it is simply not

solve 4x2+12x =0by using quadratic formula

Mr.Carr is installing wall-to-wall carpeting in a room that measures 12 1/2ft. by 9ft. How much will it cost Mr. Carr if he purchases carpet priced at $26.00 per square yard?


what is quarditic equation


In the earlier two sections we've talked quite a bit regarding solving quadratic equations.  A logical question to ask at this point is which method has to we employ to solve a giv