Choosing and rejecting inequality

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In summary, the conversation is about finding the exact values for which the equations y = |(x-2)(x-4)| and y = 6 - 2x are equal. The solution involves solving a quadratic equation and considering two cases: 2 < x < 4 and x < 2 or x > 4. The expert suggests discarding one of the solutions based on the given restrictions. The individual expresses understanding and plans to practice more.
  • #1
thomas49th
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Homework Statement


y = |(x-2)(x-4)| and y = 6 -2x

find the exact values for which these two equation equal each other


Homework Equations





The Attempt at a Solution



Right I got it down to

[tex]2 \pm \sqrt{2}[/tex] and [tex]4 \pm \sqrt{2}[/tex] and

and I've sketched the graph, however how do i work out which values to reject and which to use?

Thanks :)
 
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  • #2
You should have two cases: one for 2 < x < 4 and the other for x < 2 or x > 4. These two cases correspond to the intervals where (x - 2)(x - 4) is negative and positive, respectively.

For the case 2 < x < 4, I solved the quadratic equation x^2 - 8x + 14 = 0. My solutions were 4 +/- sqrt(2). Since 4 + sqrt is larger than 4, it doesn't meet the restriction that 2 < x < 4, so I would discard it.

Is that enough help?
 
  • #3
yes, thankyou I think I see what your saying

I will do some pratice questions

Thanks :)
 

Related to Choosing and rejecting inequality

1. What is "Choosing and rejecting inequality"?

"Choosing and rejecting inequality" is a concept that refers to the conscious and deliberate actions of individuals or institutions in either perpetuating or dismantling systems of inequality within society. It involves the choice to either accept and participate in unequal systems or actively reject and work towards creating more equitable systems.

2. How does inequality impact society?

Inequality can have significant negative impacts on society, including perpetuating cycles of poverty, limiting access to resources and opportunities, and creating social divisions and conflicts. It can also lead to feelings of injustice and inequality, leading to unrest and instability within communities.

3. What factors contribute to the perpetuation of inequality?

There are many factors that can contribute to the perpetuation of inequality, including societal structures and systems, cultural beliefs and biases, and individual actions and choices. Inequalities can also be reinforced and maintained through policies and institutions that favor certain groups over others.

4. How can individuals work towards rejecting inequality?

Individuals can work towards rejecting inequality by educating themselves about systemic inequalities and their impact, actively challenging and questioning unequal systems and structures, and advocating for policies and actions that promote equality and justice for all members of society.

5. What role does science play in addressing inequality?

Science plays a crucial role in addressing inequality by providing evidence and data that can inform policies and actions aimed at reducing inequalities. It also allows for a better understanding of the root causes and impacts of inequality, and can contribute to the development of solutions and interventions to address it.

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