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

Thirty percent of the students in a mathematics clas, Thirty percent of the...

Thirty percent of the students in a mathematics class received an “A.” If 18 students received an “A,” which of the following represents the number of students in the class?

Using transformation sketch the graph, Using transformation sketch the grap...

Using transformation sketch the graph of each of the following.                                             g ( x ) = - x 2 Solution (a)  Depending on the placement of

Ratios, How do you simplfly 25 and 15 if u say 5 and the teacher thinks it'...

How do you simplfly 25 and 15 if u say 5 and the teacher thinks it''s wrong?

Linear Equations in Linear Algebra, Question 1 [7 marks] The reduced row ec...

Question 1 [7 marks] The reduced row echelon form of ? ? ? ? ? ? ? ? ? ? ? ? 3 4 17 22 1 2 5 row a b A is equal to ? ? ? ? ? ? ? ? ? ? ? ? 0 0 0 0 0 0 1 2 1 2 0 3 R . (a) What can

Ratios, Lee is taking some friends on a picnic. They''ll need to follow a p...

Lee is taking some friends on a picnic. They''ll need to follow a path to get to the picnic spot. A map of the path is based on a scale of 1:30,000, in cm. If the path is 12 cm on

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