What is the value of M when |x|≤ 3 in the inequality (x^2+2x+1)/(x^2+3) ≤ M?

In summary: It turns out that there is a convenient way to solve such inequalities, which you can read about in my response to your other post.In summary, a value of M for the inequality |(x2+2x+1)/(x2+3)|≤ M can be found when |x|≤ 3. However, the statement that |u+v| = |u| + |v| is not always true. The absolute values in the inequality can be removed, and a quadratic inequality can be solved using a convenient method.
  • #1
altwiz
2
0
1. |(x2+2x+1)/(x2+3)|≤ M. Find the value of M when |x|≤ 3.



2. |u+v|=|u|+|v|



3. I understand that you start off by distributing the absolute value symbols into the individual terms as above. Then you maximize the numerator, using 3 as the value for x. However, my professor then minimized the denominator by using 0 as the value for x. This makes M = 240/3. What I do not understand is how you can use 2 different values of x to determine one value for M. Is there a value of x then that gives you M as the outcome in the L.H.S.?
 
Physics news on Phys.org
  • #2
altwiz said:
1. |(x2+2x+1)/(x2+3)|≤ M. Find the value of M when |x|≤ 3.



2. |u+v|=|u|+|v|



3. I understand that you start off by distributing the absolute value symbols into the individual terms as above. Then you maximize the numerator, using 3 as the value for x. However, my professor then minimized the denominator by using 0 as the value for x. This makes M = 240/3. What I do not understand is how you can use 2 different values of x to determine one value for M. Is there a value of x then that gives you M as the outcome in the L.H.S.?

Is x2 supposed to be x2? If so, either use the palette at the top of the input screen (as I just now did), or else write x^2.

Your statement |u+v| = |u| + |v| is false! For example, 0 = |1 + (-1)| ≠ |1| + |-1| = 2.
 
  • #3
As Ray already mentioned, your equation |u + v| = |u| + |v| is false.

The absolute values in your inequality can be removed, because x2 + 2x + 1 ≥ 0 for all real x, and x2 + 3 > 0 for all real x.
 
  • #4
I knew something was wrong with this question. Thank you for your replies, I will ask my professor for further clarification.
 
  • #5
altwiz said:
I knew something was wrong with this question. Thank you for your replies, I will ask my professor for further clarification.
Why? I don't think there's anything wrong with the question. Our complaint was with what you wrote as a relevant equation.

After doing some simplification, you wind up with a quadratic inequality.
 

Related to What is the value of M when |x|≤ 3 in the inequality (x^2+2x+1)/(x^2+3) ≤ M?

1. What is inequality maximization?

Inequality maximization is a concept used in economics and social sciences that refers to the process of increasing the gap between the richest and poorest members of a society. This can be achieved through various means, such as policies, economic systems, and social structures.

2. Why is inequality maximization a concern?

Inequality maximization can lead to a wide range of negative consequences for individuals and societies. It can result in social and political unrest, hinder economic growth, and contribute to health and educational disparities. Furthermore, it can undermine social cohesion and perpetuate discrimination and injustice.

3. What factors contribute to inequality maximization?

There are multiple factors that can contribute to inequality maximization, including economic policies, technological advancements, globalization, and social structures. For example, tax cuts for the wealthy, lack of access to quality education and healthcare for marginalized communities, and discrimination in hiring practices can all contribute to increasing inequality.

4. Can inequality maximization be reversed?

Yes, inequality maximization can be reversed through various means, such as implementing progressive tax policies, investing in education and healthcare for all, and promoting equal opportunities in the workforce. However, it requires a comprehensive and coordinated effort from governments, businesses, and individuals to address the root causes of inequality.

5. How can scientists contribute to addressing inequality maximization?

Scientists can play a crucial role in addressing inequality maximization by conducting research and providing evidence-based recommendations to policymakers. They can also use their platform to raise awareness about the negative impacts of inequality and advocate for more equitable policies and systems. Additionally, scientists can collaborate with communities and organizations to develop innovative solutions to reduce inequality and promote social justice.

Similar threads

Need help in manipulating rational absolute value inequalities
    • Precalculus Mathematics Homework Help
Replies
11
Views
1K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
    • Precalculus Mathematics Homework Help
Replies
3
Views
358
Where Do the Graphs of |3x-2| and 1/x Intersect and Diverge?
    • Precalculus Mathematics Homework Help
Replies
4
Views
1K
Solving for ##x## for a given inequality
    • Precalculus Mathematics Homework Help
Replies
3
Views
796
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
    • Precalculus Mathematics Homework Help
Replies
10
Views
1K
Solving an absolute value quadratic inequality
    • Precalculus Mathematics Homework Help
Replies
9
Views
822
How Do You Solve Complex Absolute Value Inequalities?
    • Precalculus Mathematics Homework Help
Replies
4
Views
1K
Absolute Value (algebraic version)....1
    • Precalculus Mathematics Homework Help
Replies
2
Views
888
Absolute Value (algebraic version)....2
    • Precalculus Mathematics Homework Help
Replies
7
Views
1K
Possible values an expression can take : ##\dfrac{x^2-x-6}{x-3}##
    • Precalculus Mathematics Homework Help
Replies
7
Views
778

Hot Threads

Recent Insights

Back
Top