# Linear Equation: Removing Negative Variables

• July 15th 2012, 07:15 AM
allyourbass2212
Linear Equation: Removing Negative Variables
Problem:
$4x-2>5x+1$

$-x>3$

$x<-3$

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

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

and in addition since we multiplied by a negative quantity within an inequality we flip the sign to
$x<-3$

Is this correct?
• July 15th 2012, 07:25 AM
earboth
Re: Linear Equation: Removing Negative Variables
Quote:

Originally Posted by allyourbass2212
Problem:
$4x-2>5x+1$

$-x>3$

$x<-3$

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

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

and in addition since we multiplied by a negative quantity within an inequality we flip the sign to
$x<-3$

Is this correct? <--- yes

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

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