simplify 5 - |x - 5|, given that x >5 (I'm getting "10" cuz...)

[SmackTED]

can you please simplify 5 - |x - 5|, given that x >5.

 

[pka]

can you please simplify 5 - |x - 5|, given that x >5.

Please read the guidelines for use of this site. When you do that, post your work.

Hint: If \(\displaystyle t\ge -1\) then \(\displaystyle |t+1|=t+1\).

 

[SmackTED]

Please read the guidelines for use of this site. When you do that, post your work.

Hint: If \(\displaystyle t\ge -1\) then \(\displaystyle |t+1|=t+1\).

I'm getting 10 cuz

5 - |x - 5| = 0
5 - x +5 = 0

- x + 10 = 0

x = 10

Still not sure if this right. Also, there's a hint with it: [FONT=&quot]Try choosing a test value for [/FONT][FONT=&quot][/FONT][FONT=&quot][FONT=MathJax_Math-italic]x[/FONT][/FONT][FONT=&quot] that satisfies the inequality..[/FONT]

 

[Deleted member 4993]

I'm getting 10 cuz

5 - |x - 5| = 0
5 - x +5 = 0

- x + 10 = 0

x = 10

Still not sure if this right. Also, there's a hint with it: Try choosing a test value for [FONT=MathJax_Math-italic]x[/FONT] that satisfies the inequality..

x = 10 certainly satisfies the given equation. But:

What do you get when x = 0 ?

 

[SmackTED]

x = 10 certainly satisfies the given equation. But:

What do you get when x = 0 ?

It says the answer is incorrect

 

[Deleted member 4993]

It says answer is incorrect

That is because:

Your given condition is that x>5.

So x = 0 cannot be answer (It satisfies the equation but does not satisfy the given condition)

 

[pka]

I'm getting 10 cuz
5 - |x - 5| = 0
Still not sure if this right. Also, there's a hint with it: Try choosing a test value for [FONT=MathJax_Math-italic]x[/FONT] that satisfies the inequality..

There is absolutely nothing about equaling zero on the original post.
If \(\displaystyle x>5\) then \(\displaystyle 5-|x-5|=5-(x-5)=10-x\)
Now where is the \(\displaystyle \Large =0~?\)

 

[SmackTED]

There is absolutely nothing about equaling zero on the original post.

If \(\displaystyle x>5\) then \(\displaystyle 5-|x-5|=5-(x-5)=10-x\)
Now where is the \(\displaystyle \Large =0~?\)

Thanks for helping me out. I just assumed the value of 0.

 

[mmm4444bot]

… simplify 5 - |x - 5|, given that x >5

5 - |x - 5| = 0

First you posted an expression, then you posted an equation.

If your original post shows the actual exercise, then don't set the expression equal to zero. You know x-5 is positive (because x is greater than 5). Therefore, |x-5| is the same as (x-5).

5 - (x - 5)

Simplify it. :cool:

 

[SmackTED]

First you posted an expression, then you posted an equation.

If your original post shows the actual exercise, then don't set the expression equal to zero. You know x-5 is positive (because x is greater than 5). Therefore, |x-5| is the same as (x-5).

5 - (x - 5)

Simplify it. :cool:

What if |6 - X| - 9, Given that X > 6

Will |6 - X| be (x-6)?

 

[SmackTED]

First you posted an expression, then you posted an equation.

If your original post shows the actual exercise, then don't set the expression equal to zero. You know x-5 is positive (because x is greater than 5). Therefore, |x-5| is the same as (x-5).

5 - (x - 5)

Simplify it. :cool:

Ah I got the concept behind it. If it's |6-x|-9 then it would be (x-6)-9 = x-15.

Thanks guys for helping me out

 

[mmm4444bot]

… Will |6 - X| be |6 - X|?

Those expressions are identical; is there a typo?

 

[SmackTED]

Those expressions are identical; is there a typo?

Yea, my bad.

 

[mmm4444bot]

… If it's |6-x|-9 then it would be (x-6)-9 = x-15 …

Yes, given x > 6

 

[pka]

can you please simplify 5 - |x - 5|, given that x >5.

\(\displaystyle 5-|x-5|=\begin{cases}5-(x-5) & x\ge 5 \\ 5-(5-x) & x<5\end{cases}\)

\(\displaystyle 5-|x-5|=\begin{cases}10-x & x\ge 5 \\ x & x<5\end{cases}\)