Question

Solve for n: -6(n -8) = 4(12 -5n) + 14n.​

Answer 1

This is a very classical type of equation in which, the solution is basically any number and it is known as an "Identity". So it has infinite solutions

Explanation:

• Apply the distributive law to both sides of the equation:

-6(n-8) = 4(12-5n)+14n

-6n-6*(-8) = 4*12+4*(-5n) + 14n

• Reduce similar terms

-6n+48=48-20n+14n

-6n+48=48-6n

• From here it is clear them to see that by adding -48 and 6n to both sides one obtains the identity 0 = 0

-6n+48=48-6n

-6n +6n + 48 -48 = 48 -48 - 6n + 6n

0 = 0

• So every time you find this kind of problem and after reducen the equation you end up with a true statement, then the equation has infinite solutions

Answer 2

infinite solutions

Explanation:

Given

- 6(n - 8) = 4(12 - 5n) + 14n ← distribute parenthesis on both sides

- 6n + 48 = 48 - 20n + 14n, that is

- 6n + 48 = 48 - 6n ( add 6n to both sides )

48 = 48 ← True

This indicates that the equation is true for any value of n