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

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

Algebra topics.., I''m starting to learn about the Pythagorean Theorem. I n...

I''m starting to learn about the Pythagorean Theorem. I need help with just the basics..

Differential Equations.., Differential Equations, Mathematics 1....

Differential Equations, Mathematics 1.Verify Liouville''''s formula for y "-y" - y'''' + y = 0 in (0, 1)

Help, 2. ABCD was a square sheet of paper, 6 cm on a side. As shown, corner...

2. ABCD was a square sheet of paper, 6 cm on a side. As shown, corner D was folded to point F on the diagonal BD. The area of triangle EFG equals the area of the shaded L-shaped po

Example of equations with radicals, Solve x =√(x+ 6) . Solution In ...

Solve x =√(x+ 6) . Solution In this equation the fundamental problem is the square root.  If it weren't there we could do the problem.  The whole procedure that we're going

Determine the zeroes of polynomials, Example : determine the zeroes of foll...

Example : determine the zeroes of following polynomials. P ( x)= 5x 5 - 20x 4 +5x3 + 50x2 - 20x - 40 = 5 (x + 1) 2 ( x - 2) 3 Solution In this the factoring has been

Writing linear equations, If you sell a kayak for $400 and your sales per d...

If you sell a kayak for $400 and your sales per day averages $5200. Assume the sales per day is a linear function of price of kayak. write an equation describing the relationship.

Slopes, why is the slope of two perpendicular line a negative reciprocal

why is the slope of two perpendicular line a negative reciprocal

Joe, .what is the average rate of change if f(x) = 4x + 6 .

.what is the average rate of change if f(x) = 4x + 6 .

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