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

..addition, what is 300000000000000000000+612222

what is 300000000000000000000+612222

Standard deviation, what is the standard deviation of a graph

what is the standard deviation of a graph

Eponents, How do you write 14x14x14x14x14x14x14= in exponential form?

How do you write 14x14x14x14x14x14x14= in exponential form?

Completing the square process, As a last topic in this section we have to b...

As a last topic in this section we have to briefly talk about how to take a parabola in the general form & convert it into the following form

Angles and sides, what is the missing angle of 37 degree and 92 drgees

what is the missing angle of 37 degree and 92 drgees

5th, 2 3/4 + 1 1/4 =

2 3/4 + 1 1/4 =

Polynomilas, i dont get them i need help

i dont get them i need help

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