Question

5n + 3/4n = 2 Solve for n

Answer 1

Flat out answer: 8 / 23

This problem requires you to combine like terms, which essentially means to combine same types of variables.

For example, 2x + 3x - 5y is an equation that is not yet simplified. 2x and 3x both have the same sharing variable labeled as "x". These can be combined to become 5x. Therefore this equation can be simplified to 5x - 5y. You cannot do anything with 5x and 5y because the variable "x" and the variable "y" are different, therefore you cannot combine like terms.

Using this simple algebraic property, we can add 5n and 3/4n together because they share the variable "n". This gives us 5.75n (since 3/4 as a decimal is 0.75). Now your equation is 5.75n = 2 and all you need to do is divide 2 by 5.75 and you get your value for n!

So,

2 ÷ 5.75 = 0.347826087

which is not the prettiest answer, so let's use our knowledge of fractions.

2 ÷ (5 and 3/4ths)

equals

2 ÷ (23/4ths)

which is

2 × (4/23)

which can be shown as

(46/23) × (4/23)

which is this ugly fraction

(184/529)

which is simplified to

8/23

the value n equals 8/23rds!

hope this helps

Answer 2

5n+3/4n=2
20n+3n/4=2
23n/4=2
23n=8
n=8/23