#### why do we have to switch the inequality symbol when dividing by a negative number

understanding why we have to switch the inequality symbol when dividing by a negative number

Naomi Rivera

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understanding why we have to switch the inequality symbol when dividing by a negative number

Qalaxia QA Bot

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I found an answer from math.stackexchange.com

Why **do we reverse inequality** sign when **dividing** by **negative number**?

Dec 28, 2011 **...** What **is** going in terms of number line that **will** help me **understand** the concept
better? ... **Dividing** by a **negative number is** the same as **dividing** by a positive ...
same as **switching** the **signs** of the numbers on both sides of the **inequality**, .....
**we**'**ve** reduced the comparison to an application of the law of **signs**, ...

For more information, see Why **do we reverse inequality** sign when **dividing** by **negative number**?

Qalaxia QA Bot

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**Do I flip** the **inequality** sign when **dividing** a **negative** by a positive ...

Apr 1, 2017 **...** ... divisor (the **number** doing the **division**) **is** a **negative**, **you need** to **flip** ... **signs**
when multiplying by a **negative** on both sides of an **inequality**?

For more information, see **Do I flip** the **inequality** sign when **dividing** a **negative** by a positive ...

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Why **does** the sign **get** reversed in an **inequality**?

Apr 18, 2017 **...** Applying a strictly decreasing function on an **inequality** reverses it. ... to the right (
e.g 5 vs. 3), after the multiplication, **are negative numbers** further to the left (i.e. −
5 vs. − 3 ), showing the **inequality must change** direction. ... **Dividing** of positive
number by **negative number** gives a **negative number**. Let a > b .

For more information, see Why **does** the sign **get** reversed in an **inequality**?

Qalaxia QA Bot

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I found an answer from www.quora.com

Why **must** one **switch signs** when multiplying by a **negative** on both ...

**Do I flip** the **inequality** sign when **dividing** a **negative** by a positive? ... When **you**
**have** placed 7 and -7 on the **number** line, it **will** be clear that 7 > 5, but that -7 ...

For more information, see Why **must** one **switch signs** when multiplying by a **negative** on both ...

Qalaxia Knowlege Bot

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I found an answer from en.wikipedia.org

**Inequality** (mathematics) - Wikipedia

In mathematics, an **inequality is** a relation that holds between two **values** when
they **are** .... If c **is negative**, then multiplying or **dividing** by c inverts the **inequality**:
... terms by same nonzero **number** and **reverse** all **inequalities** if that **number is**
**negative**. ... For example, for any positive **numbers** a1, a2, …, an **we have** H ≤ G
≤ A ...

For more information, see **Inequality** (mathematics) - Wikipedia

Qalaxia Knowlege Bot

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I found an answer from en.wikipedia.org

Cancelling out - Wikipedia

Cancelling out **is** a mathematical process used for removing subexpressions from
a mathematical expression, when this removal **does** not **change** the meaning or
the value of the expression because the subexpressions **have** equal and ... This
**is** because if b were a **negative number** then **dividing** by a negative **would** ...

For more information, see Cancelling out - Wikipedia

Qalaxia Knowlege Bot

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I found an answer from answers.yahoo.com

explain why **you flip** the **inequality symbol** when **you** multiply or ...

When **you are** multiplying / **dividing** by a **negative number**, **you are** taking the
**negative value** of every term ... That's why **we change** the direction of the
**inequality symbol**. ... Obviously that's not true... **you need** to **flip** the '<' also.

For more information, see explain why **you flip** the **inequality symbol** when **you** multiply or ...

Qalaxia Knowlege Bot

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I found an answer from answers.yahoo.com

Math homework help (**inequalities**)? | Yahoo Answers

Conclusion: Even if one side **is** 0, **you** still **have** to **reverse** the **inequality symbol** if
**you** multiply or **divide** by a **negative number**. Source(s):.

For more information, see Math homework help (**inequalities**)? | Yahoo Answers

Diego Barcenas

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Sangeetha Pulapaka

0

The reason we have to do this is so that we get the correct solution of the inequality

Let us say we have an inequality -x\lt 1

Check the value of x, when we divide with a negative number on both sides of the inequality and flip the inequality

We get,

\frac{-x}{-1} \gt \frac{1}{-1} (flip the inequality)

to get

x \gt -1

Let us see what happens when we divide with a negative number on both sides and do not flip the inequality.

\frac{-x}{-1} \lt \frac{1}{-1}

x \lt -1

We get a different solution, when we do not reverse the sign of the inequality when we divide with a negative number.

How do we know which is the correct solution? Simple, check by graphing. You will see that the graph of -x \lt 1 will be the same as the graph x\gt -1 as both give the same solution.