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Why is it necessary to reverse the inequality symbol when dividing both sides of an inequality by a negative number provide an example?
Wiki User
∙ 11y ago
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 = -3
2/-1 = -2
So 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.
Wiki User
∙ 11y ago
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Why must you flip the inequality symbol when you divide by a negative number?
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.
When you multiply both sides of any inequality by a negative number you need to the inequality symbol?
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.
Solve the inequality negative 3p is greater than 105?
-3p > 105 divide both sides by -3 and remember that when multiplying or dividing by a negative number, you reverse the sense of the inequality: p < -35 To check to make sure the answer makes sense, select a value of p that is less than -35. For example, -100: (-3)(-100) > 105 300 > 105 which is true.
Why it is necessary to reverse the inequality symbol when multiplying both side of an inequality by a negative number?
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.
What is the effect of multiplying both sides of an inequality by a negative number?
It changes the direction of the inequality.
What happens to the inequality when it is multiplied by a negative number?
The inequality is "flipped" when multiplied by a negative number. For example, if x > y and a is a negative number, then ax < ay.
How the solution for an inequality is different from the solution for a equality?
The main difference is that if you multiply or divide by a negative number, you need to simultaneously invert the inequality - for example, a less-than sign becomes a greater-than sign. Example: -2x < 15 Multiplying by -1/2 (equivalent to dividing by -2): x > 7.5
When should the inequality sign be flipped?
when you divide the inequality by a negative number, for example -2x > 50 then x < -25
Why must you flip the inequality symbol when you divide by a negative number?
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.
When you multiply both sides of any inequality by a negative number you need to the inequality symbol?
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.
Solve the inequality negative 3p is greater than 105?
-3p > 105 divide both sides by -3 and remember that when multiplying or dividing by a negative number, you reverse the sense of the inequality: p < -35 To check to make sure the answer makes sense, select a value of p that is less than -35. For example, -100: (-3)(-100) > 105 300 > 105 which is true.
Why it is necessary to reverse the inequality symbol when multiplying both side of an inequality by a negative number?
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.
Do the same rules apply when you solve equations and inequalities?
Almost. There's one new rule, which is that whenever you multiply or divide by a negative number, you have to flip the inequality sign. To see why, try achieving the same result without this step, using positive factors and subtraction: the equation must effectively flip itself around the sign.
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.
Why it is necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number Provide an example to support your explanation?
"<" 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
What is the effect of multiplying both sides of an inequality by a negative number?
It changes the direction of the inequality.
Does the inequality sign change with equations?
the inequality sign will only change in an equation if you are multiplying or dividing by a negative number... for example if you have the equation -1x+2>3 you would subtract by 2 you would have -1x>1 the next step is -1x>1 -1 -1 your dividing by -1 so the sign flips from greater than to less than (it can go less than to greater than too) and your final answer would be x<-1
