Modulus

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Vikash

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Can 2|x+5| be expanded just like expanding 2(x+5) in parenthesis?? to give 2x+10.
 
Vikash said:
Can 2|x+5| be expanded just like expanding 2(x+5) in parenthesis?? to give 2x+10.
Click to expand...
You should know that \(|a\cdot b|=|a|\cdot|b|\) so that
\(\bf 2\cdot|x+5|=|2|\cdot|x+5|=|2(x+5)|=|2x+10|\)
 
Assuming your notation means absolute value of x + 5, the answer is NO.

[MATH]|\ x + 5\ | = \\ x + 5 \text { if } x \ge -5 \text {, but}\\ -(x + 5) \text { if } x < - 5.[/MATH]
 
pka said:
You should know that \(|a\cdot b|=|a|\cdot|b|\) so that
\(\bf 2\cdot|x+5|=|2|\cdot|x+5|=|2(x+5)|=|2x+10|\)
Click to expand...
What is 2 was replaced by a negative number ? For example -2 | x+5 | ...can it be expanded in the same way?
 
Vikash said:
What is 2 was replaced by a negative number ? For example -2 | x+5 | ...can it be expanded in the same way?
Click to expand...
You must be extremely careful.
\(|x+5|=x+5\text{ if }x\ge -5\text{ and is }=-x-5\text{ if }x<-5\).
So what would \(-2|x+5|~?\)
 
pka said:
You must be extremely careful.
\(|x+5|=x+5\text{ if }x\ge -5\text{ and is }=-x-5\text{ if }x<-5\).
So what would \(-2|x+5|~?\)
Click to expand...
Yes sir what would happen?....your explanations are great?
 
Can you answer your own question? "What would happen?"

If \(\displaystyle x\ge -5\) then \(\displaystyle x+ 5\ge 0\) so |x+ 5|= x+ 5. In that case \(\displaystyle -2|x+ 5|= -(2x+ 10)\).

But if \(\displaystyle x< -5\) then \(\displaystyle x+ 5< 0\) so |x+ 5|= -(x+ 5)= -x- 5 In that case, -2|x+ 5|= -2(-x- 5)=2x+10.
 
If 2|x+5| = 2(x+5) = 2x+10 then the absolute value bars have no special meaning as they can be replaced with parenthesis. Do you believe this?

Also you can check your own work.

Suppose x= 4. Then 2|x+5| = 2|4+5| = 2|9| = 2*9 = 18. Now 2(x+5) = 2(4+5) = 2(9) = 18.

But if x = -7, 2|-7+5| = 2|-2| = 2(2) = 4 while 2(-7+5) = 2(-2) = -4.

So is 2|x+5| = 2(x+5)?
 
Vikash said:
Can 2|x+5| be expanded just like expanding 2(x+5) in parenthesis?? to give 2x+10.
Click to expand...
Did you mean:

Can 2|x+5| be expanded just like expanding 2(x+5) in parenthesis?? to give |2x+10|.?
 
Jomo said:
If 2|x+5| = 2(x+5) = 2x+10 then the absolute value bars have no special meaning as they can be replaced with parenthesis. Do you believe this?

Also you can check your own work.

Suppose x= 4. Then 2|x+5| = 2|4+5| = 2|9| = 2*9 = 18. Now 2(x+5) = 2(4+5) = 2(9) = 18.

But if x = -7, 2|-7+5| = 2|-2| = 2(2) = 4 while 2(-7+5) = 2(-2) = -4.

So is 2|x+5| = 2(x+5)?
Click to expand...
NO IT IS NOT?
 
Subhotosh Khan said:
So, to wrap up:

(+2)*|x - 5| = |2x + 10|​

However,

(-2) * |x + 5| ╪ |-2x - 10|​
​
Why?
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Because |x+5| is always positive and multiplying it by -2 makes the LHS negative but it is not equal to the right hand side because |-2x-10| is ALWAYS POSITIVE so a negative number cannot be identical to a positive so it is not equal to...
 
Vikash said:
Because |x+5| is always positive and multiplying it by -2 makes the LHS negative but it is not equal to the right hand side because |-2x-10| is ALWAYS POSITIVE so a negative number cannot be identical to a positive so it is not equal to...
Click to expand...
Correct .... very nicely explained.
 
Sorry but I do Not agree that absolute value of something is always positive. That simply is not true? Who told you this?

For example if x=-7, then compute |x+7| and decide if the answer is positive.
 
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