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For the same reason you must flip it when you multiply by a negative number. An example should suffice.

2 < 3

If you multiply by -1, without switching the sign, you get:

-2 < -3,

which is wrong. Actually,

-2 > -3.

Look at a number line if you are not sure about this - numbers to the left are less than numbers further to the right.

Dividing by a negative number is the same as multiplying by the reciprocal, which in this case is also negative.

These signs are strictly the "Greater than" and "Less than" signs. The inequality sign is an = with a / stroke through it. If you divide an inequality by -1 it remains an inequality.

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Q: Why must you flip the inequality symbol when you divide by a negative number?

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Flip it around

The inequality symbol doesn't change direction in this case.Note that that is the same as adding a positive number.Note also that if you MULTIPLY or DIVIDE by a negative number, then you need to change the direction of the inequality symbol.

You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.

Always.

Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5

When multiplying or dividing a negative number or variable.

Yes.

When a side is multiplied or divided by a negative number.

When the two sides of the inequality are multiplied or divided by a negative number or term or expression.

u only reverse the sign when u multiply or divide by a NEGATIVE number...otherwise u don't change the direction

Yes, it is true.

Because your multiping the inverse to both sides

When an Inequality expression is multiplied (or divided) by a negative number then the Inequality sign is reversed. Example : -9x < 18 : -x < 2 : x > -2........as both sides have been multiplied by -1.

Let us look at an example. Here is an inequality: 3 is greater than 2.We write this as: 3 > 2.Now let us divide both numbers by a negative number. Let us divide by -1 to keep things as simple as possible.3/-1 = -32/-1 = -2So now the sign of the inequality must be reversed:-3 < -2.-3 is smaller than -2 and so the sign was reversed to show this. This holds true for any example we can think of.Why is this so?If we were to divide two numbers by a positive number then we would not need to change the sign of the inequality. 4 > 2. (divide by 2) 2 > 1.However, when we divide a positive number by a negative the result is always negative. A number that was higher when positive will be lower when negative.Think of a number as representing the distance from 0.4 is further away from 0 than 3 is. When the distance is greater in a positive way then the number is larger. However when the difference is greater in a negative way, such as with -4 and -3 (-4 is further away from 0) then the number is smaller.This is what happens when we divide by a negative number and so the inequality sign must be reversed to show this.

You need to reverse the inequality symbol when multiplying both sides of an inequality by a negative number because you are changing the sign of both sides of the equation. Since inequality, such as "less than", means "to the left of" on the number line (where left is minus and right is plus) then a number that is less than another will be greater than the other if the signs were reversed. Example: 3 is less than 4, but -3 is greater than -4.

It changes the direction of the inequality.

The easiest way is to "flip" the inequality symbol end divide by the negative number:Example:6 < 3 - 3s6 - 3 < 3 - 3s -33 < -3s Method a) Divide by negative coefficient and flip the inequality symbol3/-3 > -3s/-3-1 > s or s< -13 < -3s Method b) Full algorithm, eliminate -3s by adding 3s on both sides3 +3s < -3s + 3s3 + 3s < 03 - 3 + 3s < 0 -33s < -33s/3 < -3/3s < -1 Looks familiar? So basically if you perform the full algorithm (method b) you can understand why we flip the inequality symbol when we have to eliminate a negative coefficient but it is faster just to flip the symbol (method a)

An inequality is not a reflexive relationship.

You need to change it to the opposite direction; e.g 5 > 1; multiply both sides by -2 it becomes -10 < -2

The inequality symbol shows wich side of the equation is greater than the other. When you multiply a positive number by a negative number you get a negative result ( for instance 4 x -2 = -8 ). 4 is larger than -8. If we multiply a negative number by a negative number we get a positive number. 1) -5 > -6 . -1 (-5) < -1(-6) . 5 < 6 this is a true statement 2) 5 > -6 . -1 (5) < -1 (-6) . -5 < 6 this is also true 3) 6 > 5 . -1 (6) < -1 (5) . -6 < - 5 this one works too

If you want that as an inequality, you write:x <= -10 You can replace "<=" with the corresponding inequality symbol (less than or equal).

The inequality symbol.

Because when you fit in the variables, it wouldn't be true. therefore, you have to flip the inequality sign For example, 3 > 2 True 3(-2) > 2(-2) -6 > -4 False If you change the direction of the inequality symbol, in the same time that you multiply by a negative number, then you find a true statement. 3 > 2 True 3(-2) < 2(-2) -6 < -4 True This is because the greater the absolute value of a negative number, the lesser it is, while the opposite is true for a positive number. When you multiply by a negative, a very large number becomes very small, or the opposite.

"<" means "farther to the left on the number line " and ">" means "farther to the right on the number line". Multiplying by a negative number switches the sign, which is a reflection that turns left into right. Double switch example: 1<2 multiply this by (-2): -2>-4 multiply this by (-1): 2<4

Think of a number line. The larger numbers are to the right and the smaller number to the left. For instance, five is less than seven. (5 < 7). When you multiply by a negative number, then the numbe with the larger absolute value is on the left, and the number with the smaller absolute value is to the right. (-5 > -7).