4(3n-2)=show your work

(2 n)/3-2/3 = n/6+4/3

(2 n)/3-2/3 = (2 n-2)/3:

(2 n-2)/3 = n/6+4/3

Put each term in n/6+4/3 over the common denominator 6: n/6+4/3  =  n/6+8/6:

(2 n-2)/3 = n/6+8/6

n/6+8/6 = (n+8)/6:

(2 n-2)/3 = (n+8)/6

Multiply both sides by 6:

(6 (2 n-2))/3 = (6 (n+8))/6

6/3 = (3×2)/3 = 2:

2 (2 n-2) = (6 (n+8))/6

(6 (n+8))/6 = 6/6×(n+8) = n+8:

2 (2 n-2) = n+8

Expand out terms of the left hand side:

4 n-4 = n+8

Subtract n from both sides:

(4 n-n)-4 = (n-n)+8

4 n-n = 3 n:

3 n-4 = (n-n)+8

n-n = 0:

3 n-4 = 8

Add 4 to both sides:

3 n+(4-4) = 8+4

4-4 = 0:

3 n = 8+4

8+4 = 12:

3 n = 12

Divide both sides of 3 n = 12 by 3:

(3 n)/3 = 12/3

3/3 = 1:

n = 12/3

The gcd of 12 and 3 is 3, so 12/3 = (3×4)/(3×1) = 3/3×4 = 4:

|  n = 4

Step-by-step explanation:

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