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

Method of elimination, Now let's move into the next technique for solving s...

Now let's move into the next technique for solving systems of equations.  As we illustrated in the example the method of substitution will frequently force us to deal with fraction

Solving for a variable, what are the steps to solving a variable like this ...

what are the steps to solving a variable like this one -3f=g for f

Integers, how to find the distance between -2 and 3 on a number line

how to find the distance between -2 and 3 on a number line

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

Determing slopes, Give the slope of each line and determine whether the 2 l...

Give the slope of each line and determine whether the 2 lines are parallel, perpendicular or neither: 4x+3y=9 and -9x+12y=0

Polynomials, Write a polynomial function in standard form with the given ze...

Write a polynomial function in standard form with the given zeros

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