# Rewriting inequality help

• danago
In summary, the inequality states that the absolute value of (x-9) minus the absolute value of x must be greater than or equal to 9. Rewritten, this means that the absolute value of (x-9) must be greater than or equal to the sum of 9 and the absolute value of x. Using the rule for absolute values, this means that x must be less than or equal to 0. However, the solution book may have excluded 0 as a solution, which could potentially be a mistake.

#### danago

Gold Member
Solve the inequality $$\left| {x - 9} \right| - \left| x \right| \ge 9$$

I started by rewriting it as:
$$\left| {x - 9} \right| \ge 9 + \left| x \right|$$

Now, for any real numbers x and y,
$$\left| {x + y} \right| \le \left| x \right| + \left| y \right|$$

According to that,
|x-9| cannot be greater than |x|+9, but it can be equal, if x and and 9 are of the same sign. The 9 is negative, so the x must also be negative, giving the solution $$x \le 0$$

Why is it that the answer book says the answer is $$x < 0$$? Why is it excluding zero? Or is it just wrong?

Thanks,
Dan.

All I can suggest is that you go back and check the problem again. If there really is a "$\ge$" sign rather than just >, obviously x= 0 is a solution. Either you miscopied the problem or the book's answer is wrong.

I have definately copied the problem correctly from the book.

This would have many solutions... first x < 0, 0< x < 9 and with x > 9.

## 1. What is "rewriting inequality"?

"Rewriting inequality" refers to the process of identifying and addressing systemic inequalities in society, particularly related to race, gender, and socioeconomic status. It involves acknowledging and challenging the ways in which certain groups are marginalized and working towards creating more equitable systems and opportunities.

## 2. How can we rewrite inequality?

Rewriting inequality involves a multifaceted approach that includes education, policy changes, and individual actions. It requires acknowledging and addressing systemic issues, advocating for marginalized communities, and actively working towards creating a more equitable society.

## 3. Why is rewriting inequality important?

Rewriting inequality is important because it recognizes and addresses the ways in which certain groups are systematically disadvantaged and marginalized. By working towards creating a more equitable society, we can promote fairness, justice, and equal opportunities for all individuals.

## 4. How can individuals contribute to rewriting inequality?

Individuals can contribute to rewriting inequality by educating themselves on systemic issues and biases, actively advocating for marginalized communities, and supporting policies and organizations that promote equity and inclusivity. They can also reflect on their own actions and biases and strive to be more inclusive and empathetic towards others.

## 5. What are some examples of rewriting inequality in action?

Some examples of rewriting inequality include implementing diversity and inclusion initiatives in companies and organizations, advocating for policy changes that promote equity and justice, and supporting grassroots movements and organizations that work towards addressing systemic inequalities. It can also involve challenging and speaking out against discriminatory practices and biases in everyday interactions.