Example of rational inequalities, Algebra

Assignment Help:

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 , ∞ )


Related Discussions:- Example of rational inequalities

Frank, Have a % 56% discount have the amount of 285.13 what was the amoun...

Have a % 56% discount have the amount of 285.13 what was the amount used to get to 285.13? How did you get?

Problem., -200t^2+3600t-6400 if the goal was to raise 8500 what would be th...

-200t^2+3600t-6400 if the goal was to raise 8500 what would be the price of each ticket?

#title.writing and using inequalities, six is at least four more than a nu...

six is at least four more than a number. write the inequality represents in this sentence

Help..., I am a 14 year old 9th grade Freshmen, I seriously need help. I am...

I am a 14 year old 9th grade Freshmen, I seriously need help. I am failing with a 49.00 grade in my class

.., (4y2)(2y)

(4y2)(2y)

Graphing and functions, Graphing and Functions        Graphing ...

Graphing and Functions        Graphing In this section we have to review some of the fundamental ideas in graphing.  It is supposed that you've seen some graphing at th

Inconsistent systems example, Inconsistent systems example Example Solv...

Inconsistent systems example Example Solve the given systems of equations. x - y = 6 -2x + 2 y = 1 Solution We can utilize either method here, although it looks l

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd