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

Mr ashley, i need help on quadraics formulas

i need help on quadraics formulas

Algebraic Equation, The sum of digits of a number is 9 If the digits of the...

The sum of digits of a number is 9 If the digits of the number are reversed the number increases by 45 What is the original number?

Solve, x=1-yto the second power

x=1-yto the second power

WORD PROBLEM, YOU EARN 15N DOLLARS FOR MOWING N LAWNS.HOW MUCH DO YOU EARN ...

YOU EARN 15N DOLLARS FOR MOWING N LAWNS.HOW MUCH DO YOU EARN FOR MOWING ONE LAWN? SEVEN LAWNS?

Algebraic reasoning, if im working out a problem that say 16 - t over 10 = ...

if im working out a problem that say 16 - t over 10 = -8 what be the answer

Grade 6 pattern math help, using T for term- p T-1,2,3,4,5,6 = 8,16,24,32,4...

using T for term- p T-1,2,3,4,5,6 = 8,16,24,32,40. Formula is T x _ +_=8, T x_+_=16 etc same 2 numbers must be used. how do i figure this out? an brackets be used or minus?

Percent, Write this decimal as a percent. .35

Write this decimal as a percent. .35

Help, Tank A contains four times as much as Tank B. Tank C contains 32 L mo...

Tank A contains four times as much as Tank B. Tank C contains 32 L more than Tank A. The three Tanks contain 482 L of water in all. How many liters of water does Tank A contain?

Quadratic function, Which shows the quadratic function f(x) = 2(x - 4)2 - ...

Which shows the quadratic function f(x) = 2(x - 4)2 - 7 in standard form?

Intro into algebra, need help on intro into algebra college homework

need help on intro into algebra college homework

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