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

Reducible to quadratic form, Solve the equation  x 4 - 7 x 2 +12 = 0 ...

Solve the equation  x 4 - 7 x 2 +12 = 0 Solution Now, let's start off here by noticing that                          x 4  = ( x 2 ) 2 In other terms, here we can

Exponential functions, Definition of an exponential function If b is an...

Definition of an exponential function If b is any number like that b = 0 and b ≠ 1 then an exponential function is function in the form,

Solve systems using method of substitution, Example   Solve following syst...

Example   Solve following systems. (a)    3x - y = 7                 2x + 3 y = 1 Solution Thus, it was the first system that we looked at above.  Already we know th

Problem solving, The sum of 2 numbers is 37.If the large is divided by the ...

The sum of 2 numbers is 37.If the large is divided by the smaller,the quotient is 3 and the remainder is 5.Find the numbers

Equivalent Ratios and Graphs, A car travels at a rate of 50 miles per hour....

A car travels at a rate of 50 miles per hour.Use equivalent ratios to graph the distance the car travels over time.Graph time on the x-axis and distance on the y-axis

Solving systems of equations by substitution, How do you find y & x equal w...

How do you find y & x equal with -4x+y=6 and -5x-y=21

Number problems, The difference of two numbers is 18. The larger number is ...

The difference of two numbers is 18. The larger number is four more than twice the smaller. What are the numbers?

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