Question 164774
3n over 4 - 1 over 3 = 2n-1 over 6
multiplied each fraction by 12 and cancelled denominators to get whole numbers
then got n=2 over 5
but when I checked answer and substituted n for 2 over 5, i didnt get an equal answer
<pre><font size = 4 color = "indigo"><b>

You solve it right but checked it wrong.

{{{3n/4-1/3=(2n-1)/6}}}

Put parentheses around every term

{{{(3n/4)-(1/3)=((2n-1)/6)}}}

Multiply every term by {{{(12/1)}}}


{{{(12/1)(3n/4)-(12/1)(1/3)=(12/1)((2n-1)/6)}}}

Cancel:
<font size = 2 color = "black">
  3           4          2
{{{(cross(12)/1)(3n/cross(4))-(cross(12)/1)(1/cross(3))=(cross(12)/1)((2n-1)/cross(6))}}}
</font>

{{{9n-4=2(2n-1)}}}

{{{9n-4=4n-2}}}

{{{5n=2}}}

{{{n=2/5}}}

Checking:

{{{(3n/4)-(1/3)=((2n-1)/6)}}}

{{{(3(2/5)/4)-(1/3)=((2(2/5)-1)/6)}}}

{{{((6/5)/4)-(1/3)=((4/5-1)/6))}}}

{{{(6/5)(1/4)-(1/3)=((4/5-5/5)/6))}}}
<font size = 2 color = "black">
  3
{{{(cross(6)/5)(1/cross(4))-(1/3)=((-1/5)/6))}}}
       2         
</font>
{{{(3/10)-(1/3)=(-1/5)(1/6)}}}

{{{3/10 - 1/3=-1/30}}}

{{{9/30 - 10/30 = -1/30}}}
{{{-1/30 = -1/30}}}

Edwin</pre>