Linear Equation: Removing Negative Variables

Problem:

$\displaystyle 4x-2>5x+1$

$\displaystyle -x>3$

$\displaystyle x<-3$

In the final step the negative variable was removed. In the book, no additional steps or explanation is given. I am assuming the correct procedure when you have a negative variable is to multiply both sides of the equation by -1.

therefore

$\displaystyle (-x)(-1) > (3)(-1)$

and in addition since we multiplied by a negative quantity within an inequality we flip the sign to

$\displaystyle x<-3$

Is this correct?

Re: Linear Equation: Removing Negative Variables

Quote:

Originally Posted by

**allyourbass2212** Problem:

$\displaystyle 4x-2>5x+1$

$\displaystyle -x>3$

$\displaystyle x<-3$

In the final step the negative variable was removed. In the book, no additional steps or explanation is given. I am assuming the correct procedure when you have a negative variable is to multiply both sides of the equation by -1.

therefore

$\displaystyle (-x)(-1) > (3)(-1)$

and in addition since we multiplied by a negative quantity within an inequality we flip the sign to

$\displaystyle x<-3$

Is this correct? **<--- yes**

In addition: You have to flip the sign when calculating the reciprocal:

Example: .............. $\displaystyle 3 < 5~\implies~\frac13 > \frac15$