# Linear Equation: Removing Negative Variables

• Jul 15th 2012, 07:15 AM
allyourbass2212
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?
• Jul 15th 2012, 07:25 AM
earboth
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: .............. $\displaystyle 3 < 5~\implies~\frac13 > \frac15$