Dividing by a negative

[marymatthews]

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For inequalities, everytime you divide by a negative number, the arrow flips?
For example,
2x + 9 > 2
2x > - 7 (does the arrow flip here since you divide by -7)
I am confused when you flip the sign, because sometimes I dont see the arrow flipped even though you should be dividing by a negative number.
Thanks

 

[Charmm]

Nope!

In this problem you divide by 2 which is the x coef; you always divide the both sides by the coef of x so you isolate the x. And, yes any time you divided by a negative number you flip the arrow

2x + 9 > 2

subtract 9 from both sides

2x > -7

divide by 2

x > -7/2

 

[immalozer]

Just to add if you have a equation like this: l2x+9l>2
To solve for X
2x+9>2 and 2x+9<-2

 

[marymatthews]

so by dividing by a negative number, they mean dividing by a negative x value. Because here:
2x > -7
x > -7/2 ... 7 is negative, but x is not, so you do not flip.... but if it was a negative x, you would flip??
such as:
-x + 9 > 2
-x > -7
x < 7

and if this was:
l2x+9l<2
it would be:

2x+9<2 and -2<2x+9

 

[Streetwolf]

Consider the fact that:

-2x > 7

Becomes:

-7 > 2x

When you add 2x to both sides and subtract 7 from both sides.

Now when you divide by 2 you get -7/2 > x.

Had you divided by -2 originally and flipped the signs, you'd have gotten that same answer.

 

[marymatthews]

thanks, so is this correct?

l2x+9l<2
it would be:

2x+9<2 and -2<2x+9

 

[mustardseed5]

yes, the last statement is true, that is was absolut value means

 

[mustardseed5]

or in one line, -2 < 2x+9 < 2