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Why can't you flip the inequality symbol when you divide by a positive number?
Wiki User
∙ 13y ago
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.
Wiki User
∙ 13y ago
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Does positive number become negative when it crosses the inequality symbol?
Yes.
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.
When do you reverse the inequality symbol in a two-step inequality?
When multiplying or dividing a negative number or variable.
What is a number x is at most -10?
If you want that as an inequality, you write:x <= -10 You can replace "<=" with the corresponding inequality symbol (less than or equal).
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.
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.
If you multiply an inequality by a negative number when should you reverse the inequality symbol?
Always.
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
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.
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.
When do you reverse the inequality symbol in a two-step inequality?
When multiplying or dividing a negative number or variable.
What is a number x is at most -10?
If you want that as an inequality, you write:x <= -10 You can replace "<=" with the corresponding inequality symbol (less than or equal).
