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Why it is necessary to reverse the inequality symbol when multiplying both side of an inequality by a negative number?
Wiki User
∙ 14y ago
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.
Wiki User
∙ 14y ago
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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.
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 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.
Why do you reverse the inequality when you multiply or divide both sides of an inequality by a negative number?
Just try it out! If 1 < 2, and you multiply both sides by -1, you get -1 ... -2. If you look at the numbers on a number line in standard position, you see that 1 is LEFT of 2 (and therefore less), while -1 is RIGHT of -2 (and therefore greater). So, -1 > -2 and the inequality sign has been reversed.
Algebra why is it necessary to reverse the inequality symbol when multiplying both sides of an inequality by a negative number?
Because your multiping the inverse to both sides
When do you reverse the inequality symbol in a two-step inequality?
When multiplying or dividing a negative number or variable.
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
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
If you multiply an inequality by a negative number when should you reverse the inequality symbol?
Always.
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
If you multiply or divide both sides of an inequality by a number you need to reverse the inequality sign?
negative flip
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.
Explain in your own words 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?
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).
How do you solve an inequality if you are left with a negative variable?
In the case of an inequality, if you mulitply by a negative number, you have to reverse the direction of the inequality. E.g.: -x < 10 becomes: x > -10 (Here, I multiplied by -1, and simultaneously reversed the direction of the inequality.)
Do you believe you would come up with a false equality if you multiply or divide an equality by a negative number?
No. Multiplying or dividing by a negative number is perfectly valid. However, please note that:Dividing by zero will most likely give you wrong results.In the case of an inequality, if you multiply or divide by a negative number, you have to reverse the sign. For example, 2 < 3; multiplying by -2: -4 > -6
