Question

How do you solve `\frac { 2n } { 3} + \frac { 5n } { 2} = \frac { 19} { 3}`?

Answer 1

Solve `n` by performing adding the fractions and isolating it.

Explanation:

Solving implies we determine the value of `x` so the equation makes sense. To do this, we will isolate the variable.

First off, I want to add the fractions. To do this, we need to find a common denominator. With no common denomiators, we resort to the LCD (lowest common denominator) and alter the terms accordingly - while making the equation true.

The LCD in this equation is `6`. So we make all variables have a term of 6. This results in multiplying the numerator and denominator with a value.

`\frac { 2n } { 3} + \frac { 5n } { 2} = \frac { 19} { 3}`

`\frac { 4n } { 6} + \frac { 15n } { 6} = \frac { 38} { 6}`

Now that we have like terms, we can now add the fractions.

`(19n)/6= 38/6`

Now we cross multiply the terms.

`114n= 228`

Now we can finally isolate `n`.

`n=2`

We can double check our work by subbing in `n=` into the original equation.

`\frac { 2n } { 3} + \frac { 5n } { 2} = \frac { 19} { 3}`

`\frac { 2(2) } { 3} + \frac { 5(2) } { 2} = \frac { 19} { 3}`

`\frac { 4 } { 3} + \frac { 10 } { 2} = \frac { 19} { 3}`

We still need to find LCD.

`\frac { 8 } { 6} + \frac { 30 } { 6} = \frac { 38} { 6}`

`\frac { 38 } { 6} = \frac { 38} { 6}`

Thus, we can conclude that `n=2`.

Hope this helps :)