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Because if you do flip the symbol when you divide or multiply by a positive, the statement will no longer be true.
Just to get the clear picture here, look at this example.
4>2
4 is greater than 2, which is true, so what if we divide both sides by 2 and switch the symbol...
we would have..
2<1
2 is less than 1...which is wrong and doesn't make sense. It all has to do with trying to make things a true statement.
What else can I help you with?
Does positive number become negative when it crosses the inequality symbol?
Yes.
If both sides of an inequality are multiplied of divided by the same positive number the direction of the inequality symbol is?
If both sides of an inequality are multiplied or divided by the same positive number, the direction of the inequality symbol remains the same. For example, if you have ( a < b ) and you multiply both sides by a positive number ( c ), the inequality remains ( ac < bc ). This property holds true for all positive numbers, ensuring the relationship between the two sides is preserved.
How do you know when to reverse the direction of an inequality symbol?
u only reverse the sign when u multiply or divide by a NEGATIVE number...otherwise u don't change the direction
How does an inequality symbol act differently than an equal symbol?
An inequality is not a reflexive relationship.
What three actions can cause the direction of an inequality symbol to change?
The direction of an inequality symbol can change when you multiply or divide both sides of the inequality by a negative number, which reverses the inequality. Additionally, if you add or subtract a term that is common on both sides without affecting the inequality's balance, the direction remains unchanged. However, if the operation involves terms that can alter the order of values, such as modifying a variable's sign, the direction may also change.
What happens to the inequality symbol when you subtract a negative number?
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.
When you divide both sides of any inequality by a negative number you need to what the inequality symbol?
Flip it around
Does positive number become negative when it crosses the inequality symbol?
Yes.
If both sides of an inequality are multiplied of divided by the same positive number the direction of the inequality symbol is?
If both sides of an inequality are multiplied or divided by the same positive number, the direction of the inequality symbol remains the same. For example, if you have ( a < b ) and you multiply both sides by a positive number ( c ), the inequality remains ( ac < bc ). This property holds true for all positive numbers, ensuring the relationship between the two sides is preserved.
How do you divide by a negative in an inequality?
You divide as normal BUT you change the direction of the inequality symbol, so that < becomes > and conversely.
Why is it necessary to reverse the inequality symbol when dividing both sides of an inequality by a negative number provide an example?
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.
When you divide both sides of an inequality by a negative number you need to blank the inequality symbol?
Flip. You need to reverse the inequality when multiplying or dividing by a negative. -2x < 10 (-1)*(-2x) < (-1)*10 2x > -10 x > -5
If you multiply an inequality by a negative number when should you reverse the inequality symbol?
Always.
How do you know when to reverse the direction of an inequality symbol?
u only reverse the sign when u multiply or divide by a NEGATIVE number...otherwise u don't change the direction
How does an inequality symbol act differently than an equal symbol?
An inequality is not a reflexive relationship.
What three actions can cause the direction of an inequality symbol to change?
The direction of an inequality symbol can change when you multiply or divide both sides of the inequality by a negative number, which reverses the inequality. Additionally, if you add or subtract a term that is common on both sides without affecting the inequality's balance, the direction remains unchanged. However, if the operation involves terms that can alter the order of values, such as modifying a variable's sign, the direction may also change.
When solving an inequality when is it necessary to change the direction of the inequality symbol?
When the two sides of the inequality are multiplied or divided by a negative number or term or expression.
