+0

# solve |2x-1|=|3x+5|

0
424
1

solve |2x-1|=|3x+5|

Guest Jun 27, 2015

#1
+91510
+10

$$\\|2x-1|=|3x+5|\\\\ 2x-1=3x+5\qquad or \qquad 2x-1=-(3x+5)\\\\ 2x=3x+6\qquad or \qquad 2x-1=-3x-5\\\\ -x=6\qquad or \qquad 2x=-3x-4\\\\ x=-6\qquad or \qquad 5x=-4\\\\ x=-6\qquad or \qquad x=\frac{-4}{5}\\\\ check\\\\ If\;\; x=-6\\\\ |-12-1|=|-18+5|\\\\ 13=13\qquad True\\\\$$

$$\\If\;\; x=\frac{-4}{5}\\\\ |\frac{2*-4}{5}-1|=|\frac{3*-4}{5}+5|\\\\ |\frac{2*-4-5}{5}|=|\frac{3*-4+25}{5}|\\\\ |\frac{-13}{5}|=|\frac{13}{5}|\\\\ \frac{13}{5}= \frac{13}{5} \qquad True\\\\ therefore the solutions are \\\\ x=-6\;\;and \;\; x=\frac{-4}{5}\\\\$$

Here is the graphical solutions

https://www.desmos.com/calculator/rvzeay4sfu

Melody  Jun 28, 2015
Sort:

#1
+91510
+10

$$\\|2x-1|=|3x+5|\\\\ 2x-1=3x+5\qquad or \qquad 2x-1=-(3x+5)\\\\ 2x=3x+6\qquad or \qquad 2x-1=-3x-5\\\\ -x=6\qquad or \qquad 2x=-3x-4\\\\ x=-6\qquad or \qquad 5x=-4\\\\ x=-6\qquad or \qquad x=\frac{-4}{5}\\\\ check\\\\ If\;\; x=-6\\\\ |-12-1|=|-18+5|\\\\ 13=13\qquad True\\\\$$

$$\\If\;\; x=\frac{-4}{5}\\\\ |\frac{2*-4}{5}-1|=|\frac{3*-4}{5}+5|\\\\ |\frac{2*-4-5}{5}|=|\frac{3*-4+25}{5}|\\\\ |\frac{-13}{5}|=|\frac{13}{5}|\\\\ \frac{13}{5}= \frac{13}{5} \qquad True\\\\ therefore the solutions are \\\\ x=-6\;\;and \;\; x=\frac{-4}{5}\\\\$$

Here is the graphical solutions

https://www.desmos.com/calculator/rvzeay4sfu

Melody  Jun 28, 2015

### 29 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details