First, we will convert all the mixed numbers (#1 2/3#) to improper fractions (#12/3#).
#-43/24+2 2/3n=-7/4(-3/2n+1)# to
#-43/24+8/3n=-7/4(-3/2n+1)#
Let's focus on the right side of the equation (#-7/4(-3/2n+1)#)
We will distribute parentheses/brackets with: #x(y+z)=xy+xz#
In this case, #x# represents #-7/4#, #y# represents #-3/2n# and #z# represents #1#. Therefore: #-7/4*(-3/2n)cancel+ -7/4*1#
We cancel out the #+# as #+ -# is equal to #-# so the #+# is redundant.
We will apply this to #-7/4*(-3/2n)-7/4*1#:
#-(-x)=x# and #+(-x)=-x#. Therefore, the equation will now be:
#7/4*3/2n-7/4*1#.
Now we will focus on #7/4*3/2n#, which is the same as #(7*3)/(4*2)n#.
#7*3=21# and #4*2=8# so therefore the equation will be #21/8n#.
The right side is just #7/4*1# which is already equal to #7/4#.
Combine the left and right side (and the left side of the whole equation) and you will get #-43/24+8/3n=21/8n-7/4#.
Add #43/24# to both sides.
#-43/24+8/3ncolor(blue)+color(blue)43/color(blue)24=21/8n-7/4color(blue)+color(blue)43/color(blue)24#
The left side would be #8/3n#.
Let's solve the right side: #21/8n-7/4+43/24#
First, we leave #21/8n# which is #(21n)/# aside for now.
Then, change the denominator of #-7/4# and #43/24# to #24# (Make sure to multiply #6# for the numerator of #-7/4#)
#-(7*6)/24+43/24# which is #(-6*7+43)/24#
#-6*7=-42# and #-42+43=1#.
Therefore, the whole equation would be equal to #8/3n=1/24+(21n)/8#
Now we subtract #(21n)/8# from both sides
#8/3n color(blue)-(color(blue)21color(blue)n)/color(blue)8=1/24+(21n)/8color(blue)-(color(blue)21color(blue)n)/color(blue)8#
which is equal to #n/24=1/24# so #n=1#.
