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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, ...

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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?

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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 .

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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 ...

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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 ...

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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.

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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):.

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Diego Barcenas
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I think it has something to do with keeping the equation balanced, as a negative number has a lot of power, and I think that it could be necessary for the symbol switch to counter a negative value.

Sangeetha Pulapaka
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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.