Question #fb844

1 Answer
Sep 22, 2017

n=1

Explanation:

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.