Q: Is it true When dividing by a negative number the direction of the inequality symbol MUST be reversed?

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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.

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.

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.

Then the resultant vector is reversed.

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.

Related questions

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.)

When one side of the inequality is divided or multiplied by a negative number.

The direction of the inequality is reversed. Note that the if the inequality included "or equals" before, then it will after. 4 < 5 multiplied by -1 gives -4 > -5 5 >= 4 multiplied by -1 gives -5 <= -4

rotates 180 degrees

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.

Positive and negative are reversed. It will run either direction depending on which way it is wired.

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 solving an equation, you are looking for a specific answer or answers. However, when solving inequalities, you are only looking for what an answer could be (for example, your answer could be less than 5 or greater than 32).

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.

Treat inequalities like equations. Both sides can have equal amounts added or subtracted, or be multiplied or divided by numbers of equal value.There is a major exception :- When multiplying or dividing by a negative number then the inequality sign is reversed.EXAMPLE : 4x + 5 > 2x + 9 : 4x - 2x > 9 - 5 : 2x > 4 : x > 2EXAMPLE : 3 -7x < 2x + 21 : -7x - 2x < 21 - 3 : -9x < 18 : -x < 2 if this inequality is now multiplied by -1 note how the inequality sign is reversed x > -2

Then the resultant vector is reversed.

Yes, a scalar can be a negative number. For instance: c<x₁,x₂> = <cx₁,cx₂> such that <x₁,x₂> is a vector. Let c = -1 for instance. Then, we have this vector: <-x₁,-x₂> Compared to <x₁,x₂>, <-x₁,-x₂> has negative signs. In physics and mathematics, if we multiply the vector or something by a negative value scalar, then the direction of the vector is reversed, and the magnitude stays the same. If the magnitude increases/decreases, and the direction of the vector is reversed, then we can multiply the vector by any negative non-1 scalar value.