Do you only reversethe greater than or equal sign when you divide by a negative number?

Answer 1

for example:

-1 < 2
then
1 > -2

another:
x < -5
then
-x > 5

-2 x > 9
x< -9/2

s

Answer 2

Well, no. You've got to reverse it when you by a negative number too.

Most of the algebra books teach it that way. The trouble is, there's no explanation for it.

The rule of changing the direction of the inequality when you multiply or divide by a negative is actually a shortcut. When I teach it, I always do it the "long" way first, and then let the students do it the short way.

Here's an example, short way first:

Solve 14 - 3x > 20. First, subtract 14 from each side to get

-3x > 6. Now divide each side by -3 and reverse the direction of the inequality to get

x < -2 (Answer)

Now we'll do the same problem the "long" way, without reversing the direction.

Solve 14 - 3x > 20.

To do this, we want "positive" x, not negative, so we'll move the x term over to the right-hand side. At the same time, we want to move the numbers (the 20) over to the left.

To do this, add 3x - 20 to both sides, and reverse the inequality. When you do this, -3x + 3x and 20 - 20 cancel out, and you get:

14 - 20 > 3x
-6 > 3x

Notice that we reverse the inequality. Divide both sides by 3 to get

-2 > x

which you can rewrite as

x < -2 (Same answer as above, but with more detail on why the rule works)

Answer 3

That is one case
However there is another, which occurs is when taking reciprocals

eg If both the signs are positive

1/x < 2 so x > 1/2

BUT if one sign is negative

1/x < -2 means -1/2 < x < 0 only Because ANY positive number is greater than any negative number.

and 1/x > -2 means x < -1/2 OR x > 0

Finally, if the signs are both negative change to positive first by your rule and then proceed as above

eg -1/2 < -1/x
so 1/2 > 1/x
ie 2 < x

Answer 4

An example would be 15/-3 > 25/5, since the left side of the inequality would be a negative and less than the right, then yes you would reverse it.

Answer 5

Try a simple example:

6 > 4

divide by -2

6/-2 >? 4/-2

-3 >? -2

so, yes you would need to reverse the sign.

-3 < -2 correct!

Answer 6

yes, only when you divide by a negative number. when a postive is divided the swign remains the same.