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.

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 , ∞ )

Posted Date: 4/6/2013 5:33:32 AM | Location : United States

Ask an Expert

Related Discussions:- Example of rational inequalities, Assignment Help, Ask Question on Example of rational inequalities, Get Answer, Expert's Help, Example of rational inequalities Discussions

Write discussion on Example of rational inequalities
Your posts are moderated

Write your message here..

Related Questions

Equations, 5x+3y=0 5x+3y=0

Venn diagram, ``A car dealer has 22 vehicles on his lot. If 8 of the vehicl... ``A car dealer has 22 vehicles on his lot. If 8 of the vehicles are vans and 6 of the vehicles are red, and 10 vehicles are neither vans nor red, how many red vans does he have on

Solve equation by geometric standpoint, Solve each of the following.    ... Solve each of the following.                              |x - 2 | = 3x + 1 Solution At first glance the formula we utilized above will do us no good here.  It needs the

Example of work- rate problems, An office contains two envelope stuffing ma... An office contains two envelope stuffing machines. Machine A can stuff a batch of envelopes within 5 hours, whereas Machine B can stuff batch of envelopes within 3 hours. How much

Algebra 2, how do you solve a logarithm? how do you solve a logarithm?

Manipulation properties of the logarithm, For these properties we will supp... For these properties we will suppose that x > 0 and y > 0 log b ( xy ) = log b x + log b   y log b (    x/y) = log b   x - log b   y log b (x r ) = r log  x If log

Assignment 2: Financial Project, ue Week 7 and worth 55 points Five (5) ye... ue Week 7 and worth 55 points Five (5) years ago, you bought a house for $171,000, with a down payment of $30,000, which meant you took out a loan for $141,000. Your interest rate

Rearraning equations, please help I need step by step on this please help I need step by step on this

Measurement of central, how to answer how to answer

Rational expressions, I am looking the domain of g^2-6g-55/g. The denominat... I am looking the domain of g^2-6g-55/g. The denominator here can be also be written as 1g, right?