What is n

-8+4 (1+5n) = -6n-14

n = (-5) / 13

Step-by-step explanation:

Solve for n:

4 (5 n + 1) - 8 = - 6 n - 14

4 (5 n + 1) = 20 n + 4:

20 n + 4 - 8 = - 6 n - 14

Add like terms. 4 - 8 = - 4:

20 n - 4 = - 6 n - 14

Add 6 n to both sides:

20 n + 6 n - 4 = (6 n - 6 n) - 14

6 n - 6 n = 0:

20 n + 6 n - 4 = - 14

20 n + 6 n = 26 n:

26 n - 4 = - 14

Add 4 to both sides:

26 n + (4 - 4) = 4 - 14

4 - 4 = 0:

26 n = 4 - 14

4 - 14 = - 10:

26 n = - 10

Divide both sides of 26 n = - 10 by 26:

(26 n) / 26 = (-10) / 26

26/26 = 1:

n = (-10) / 26

The gcd of - 10 and 26 is 2, so (-10) / 26 = (2 (-5)) / (2*13) = 2/2 * (-5) / 13 = (-5) / 13:

Answer: n = (-5) / 13