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Why does the sign in an inequality change when you divide by a negative?
Wiki User
∙ 14y ago
Let's try an example:
2 < 4
divide both sides by -2 and you get:
-1 < -2
which is clearly false.
Another example:
-4 < -2
divide both sides by -2 and you get:
2 < 1
which is again false.
Here is a simple proof:
Assume x < y
Then subtract y from both sides:
x - y < 0
Now subtract x from both sides:
-y < -x which is the same is -x > -y
Summarizing: x < y implies that -x > -y.
Wiki User
∙ 14y ago
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Does an inequality change when you multiply by a negative?
Yes you have to flip the sign.
What happens when you multiply or divide an inequalitie by a negative number?
When an inequality is multiplied or divided by a negative number the inequality sign is reversed.Example : -x < 7 ......after multiplying by (say) -2 this becomes 2x > -14
What must you do when solving an inequality with a negative coefficient?
Divide by negative one and flip the sign eg -x > 6 / -1 /-1 x < - 6
When does the sign change in inequalities?
whenever you multiply or divide by a negative number
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 positive value you must change the direction of the inequality sign?
No. Only when you divide by a negative.
When is the only time you flip an inequality sign?
When you divide both sides of an inequality by a negative number, the inequality sign flips.
When you have to reverse the inequality sign?
The usual case is when you multiply or divide an inequality by a negative number.
When solving an inequality when do you reverse the inequality sign?
When you divide both sides by a negative value
Do you only flip the inequality when you divide by a negative number?
Yes you do, you also flip the inequality sign if you multiply by a negative # The > and < 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.
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 must reverse the inequality sign?
When solving an inequality, you must revers the inequality sign when you multiply (or divide) both sides by a negative number.
Does an inequality sign change in an equation when both sides are multipled or divided by negative number?
The sign changes if you multiply/divide by a negative number. It stays the same if you add/subtract by a negative number.
What must occur in a linear inequality when you divide or multiply by a negative number?
The inequality sign must be flipped.
If you multiply or divide both sides of an inequality by a number you need to reverse the inequality sign?
negative flip
When should the inequality sign be flipped?
when you divide the inequality by a negative number, for example -2x > 50 then x < -25
What do you do with your inequality if you divide by both sides by a negative number?
If two sides of an inequality are multiplied (or divided) by a negative number, you have to invert the sign. For example, a "less-than" sign becomes a "greater-than" sign.
