# Doubt in an inequality problem

• Thiru07
In summary, to solve the inequality (y+2)(y-3) <= 0, we need to examine two cases: y-3 <= 0 and y+2 >= 0, and y-3 >= 0 and y+2 <= 0. This gives us the solutions y <= 3 and y <= -2, respectively. However, the solution y <= 3 does not hold, as it would also include y <= -2, which is not possible. Therefore, the correct solution is y <= -2.
Thiru07

## Homework Statement

Given : (y+2)(y-3) <= 0

## The Attempt at a Solution

Now, I have y-3 <= 0 or y+2 <= 0
Hence, y <= 3 or y <= -2
But how
-2 <= y <= 3
is correct?
I think
-2 <= y <= 3
is wrong because y <= -2.
Can someone please clarify?

Thiru07 said:

## Homework Statement

Given : (y+2)(y-3) <= 0

## The Attempt at a Solution

Now, I have y-3 <= 0 or y+2 <= 0
Hence, y <= 3 or y <= -2
But how is correct?
I think is wrong because y <= -2.
Can someone please clarify?

You could draw a graph of ##(y+2)(y-3)## to see what's happening.

What happens if both ##y+2 < 0## and ##y-3 < 0##?

PeroK said:
You could draw a graph of ##(y+2)(y-3)## to see what's happening.

What happens if both ##y+2 < 0## and ##y-3 < 0##?
In that case , we will keep y < -2 and ignore y < 3.
I think I got it. We have to ignore y+2 <= 0 and y-3 >=0 as
y <= -2 and y >= 3
is not possible and keep
y >= -2 and y <= 3

Thanks PeroK :)

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Thiru07 said:
Given : (y+2)(y-3) <= 0

Now, I have y-3 <= 0 or y+2 <= 0
No, the above doesn't follow from the inequality. I think you might already have solved this inequality, but showing where you went wrong is worthwhile.
For the product of two expressions to be negative, one of them has to be negative, and the other has to be positive. Since this can happen in either of two ways, you need to examine two different cases.
Thiru07 said:
Hence, y <= 3 or y <= -2

## What is an inequality problem?

An inequality problem is a mathematical problem that involves comparing two quantities using the symbols <, >, ≤, or ≥. It indicates that one quantity is larger or smaller than the other.

## Why do inequalities sometimes involve doubt?

Inequalities can involve doubt because they are not always straightforward or clear-cut. Sometimes, there may be multiple solutions or approaches to solving an inequality, leading to uncertainty about the correct answer.

## How can I determine if my solution to an inequality problem is correct?

You can determine if your solution to an inequality problem is correct by plugging your solution back into the original problem to see if it satisfies the given inequality. If it does, then your solution is correct.

## What strategies can I use to solve an inequality problem?

There are several strategies for solving inequality problems, including graphing, algebraic manipulation, and using number lines. It is important to identify the given information and the desired outcome to choose the best strategy for solving the problem.

## What are some common mistakes to avoid when solving an inequality problem?

Common mistakes to avoid when solving an inequality problem include forgetting to flip the inequality sign when multiplying or dividing by a negative number, not considering the inequality's direction when graphing, and not checking the solution to see if it satisfies the original problem. It is also important to be careful with signs and to double-check your calculations.

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