[tex] \frac{2x}{3} - \frac{5}{6} = \frac{-5x}{12} + \frac{1}{4} [/tex]
<< Equate all the denominators with a ^minimum^ common number(12).
[tex]= \frac{4.2x}{12} - \frac{5.2}{12} = \frac{-5x}{12} + \frac{3}{12} [/tex]
<< Classify same terms to one side. The fraction that you threw to other side in the equation changes.
[tex]= \frac{8x+5x}{12} = \frac{3+10}{12} [/tex]
[tex] \frac{13x}{12} \frac{13x}{12} [/tex]
13x=13
x=13/13
x=1
So the main equation's solution set is 1.
Let's look at the options then!
1: [tex] \frac{-5}{6} = \frac{x}{4} + \frac{1}{4}[/tex]
**equate denominators
= [tex] \frac{-5}{6} - \frac{1}{4} = \frac{x}{4}[/tex]
= [tex] \frac{-10-3}{12} = \frac{3x}{12} [/tex]
=[tex]-13=3x[/tex]
x= [tex] \frac{-13}{3} [/tex]
2: [tex] \frac{2x}{3} =\frac{-5x}{12} - \frac{-7}{12}
[/tex]
[tex]8x= -5x-7[/tex]
**throw -5x left of the equation.
[tex]13x=-7[/tex]
x= [tex] \frac{-7}{13}[/tex]
3: [tex] \frac{x}{4} - \frac{5}{6} = \frac{-1}{4} [/tex]
[tex]3x-10=3[/tex]
3x=7
x=7/3
4: [tex] \frac{2x}{3} - \frac{13}{12} = \frac{-5x}{12} [/tex]
8x-13= -5x
13x=13
x=1
The correct answer is 4.
Hope it helps!
#MissionExam001
