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Given the function $$\frac{1}{2}x+\left|x-5\right|=3$$, solve for $$x$$.

(People who can answer this question will be appreciated :D)

Jeffes02  Aug 20, 2017
edited by Jeffes02  Aug 20, 2017
edited by Jeffes02  Aug 20, 2017
#1
+71
+2

Hi,I will have to use mod(x-5) for the expression  on the left hand side.To mean the modulus,or positive value of  x-5. So I can only write it like this ---  bear with me.

1/2(x) +mod(x-5) = 3     solve for  x      Solution -

Move 1/2(x) to the right hand side so that we can square both sides,and then solve the quadratic.

thus

{mod(x-5)]^2 = [3-1/2(x)]^2

x^2-10x+25  = 9-3x +1/4(x^2)         re-arrange to get

3/4(x^2) -7x+16=0

x =[ 7 plus or minus sqrt(49 -4(3/4)(16)]  / (3/2)

which simplifies to

(2/3) (7) (plus or minus 1)

= plus or minus (14/3)

frasinscotland  Aug 20, 2017
#5
+26817
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You slipped up in your simplification stage frasinscotland.

$$x = \frac{7\pm \sqrt{49-4(3/4)16}}{3/2}\rightarrow \frac{7\pm1}{3/2}$$

This leads to $$x_+=\frac{8}{3/2}\rightarrow \frac{16}{3}$$  and $$x_-=\frac{6}{3/2}\rightarrow4$$

Alan  Aug 20, 2017
#2
+178
+1

Good job! I spent hours trying to solve this in wolfram only to get paid promotions slammed in my face, and a random guest is able to solve my answer clearer than it, appreciated for clearing my problem up :D

(You can use my method for writing math expressions if you prefer:)

1.Write the formula you want to put in this forum somewhere.

2.Copy/Paste it into Desmos on the left

In which it will turn the formula you entered into LaTeX (A kind of system to write math expressions.)

3.Choose the Sigma symbol (LaTeX) option on the tool bar above.

4.Copy/Paste your formula from Desmos into the LaTeX interface.

5.Press OK.

5.Done!

(See you having a hard time dealing with brackets and spacings :) )

Jeffes02  Aug 20, 2017
#3
+92896
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Jeffes02, you REALLY need to learn to use the words  'thank you'

It is not difficult, practice in a mirror if you need to.

'Good job', sounds condescending. So don't use it.

The person who answered your question was not a 'random guest' he/she is a real person who allocated their time and knowledge to helping you.

I know that you did use the word 'appreciate'. It was good to see that but your gratitude wording definitely needs to be worked upon.

You provide heaps of great answers on the forum, I have thanked you on a number of occasions and your efforts really are appreciated.

When you ask questions it is you who needs to show gratitude. Besides being polite it will also work in your favour as people will want to answer your questions in the furure.

Melody  Aug 20, 2017
#4
+26817
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Drawing a graph is always a good idea with these sort of questions:

.

Alan  Aug 20, 2017