# Inequality Solution [ , +Part solution included]

• lovemake1
In summary, the problem is to solve the inequality l 3/(x-1) - 5 l < 4 and the attempted solution is to rewrite the inequality as -4 < 3/(x-1) - 5 < 4 and then manipulate it to get x between two numbers, but this method is not necessarily true if the numbers are not both positive or negative. Another method suggested is to use a<\frac{1}{x}<b \implies\frac{1}{a}>x>\frac{1}{b}.
lovemake1
Inequality Solution [URGENT, +Part solution included]

## Homework Statement

l 3/(x-1) - 5 l < 4

## The Attempt at a Solution

so here's where I am abit confused. since the inequality sign is not > or >= but instead in this case it is <. Therefore, x has to be between two numbers.

But when i tried to solve l 3/(x-1) - 5 l < 4, it doesn't work out.
Heres my work:

-4 < 3/(x-1) - 5 < 4
1 < 3/(x-1) < 9
x-1 < 3 < 9x-9

you see.. this is nothing where its suppose to be.
i end up getting... bigger number < x < smaller number

Use the fact that if
$$a < \frac{1}{x} < b$$

then

$$\frac{1}{a} > x > \frac{1}{b}$$ .

well here's a better question.

can i make the equation like this ?

1 < 3(x-1) < 9
x-1<3 or 3<9x-9
x < 4 or x > 4/3

Can this work too? 4/3 < x < 4

You can do that, but that method will be confusing if you ever work with inequalities that have unknowns instead of numbers.

Clarification:

$$a<\frac{1}{x}<b$$
$$\implies\frac{1}{a}>x>\frac{1}{b}$$

is only necessarily true if a and b are both negative or both positive. Sorry for the error.

## What is "Inequality Solution"?

"Inequality Solution" is a term used to describe potential solutions for issues related to inequality, such as income inequality, social inequality, or economic inequality.

## Why is inequality a problem?

Inequality can lead to a range of negative consequences, such as social unrest, decreased economic growth, and reduced opportunities for individuals. It can also perpetuate cycles of poverty and disadvantage.

## What are some potential solutions to inequality?

Potential solutions to inequality can vary depending on the specific issue, but some common solutions include policies that promote equal access to education, healthcare, and job opportunities, as well as measures to address systemic discrimination and promote economic equality.

## What role do governments play in addressing inequality?

Governments can play a significant role in addressing inequality through policies and programs that aim to reduce income disparities, provide social safety nets for marginalized populations, and promote equal opportunities for all individuals.

## What can individuals do to help address inequality?

Individuals can help address inequality by educating themselves on the issue, supporting organizations and initiatives that promote equality, and advocating for policies and practices that promote fairness and equal opportunities. Additionally, individuals can be mindful of their own actions and biases that may contribute to inequality and work towards being more inclusive and equitable in their interactions with others.

Replies
11
Views
2K
Replies
9
Views
1K
Replies
9
Views
461
Replies
5
Views
1K
Replies
7
Views
999
Replies
11
Views
1K
Replies
4
Views
2K
Replies
4
Views
993
Replies
6
Views
2K
Replies
15
Views
3K