Question

How do you solve `\frac { 3v - 7} { 2} + \frac { v - 9} { 4} = 10?`

Answer 1

Use the LCM of the two denominators to simplify the equation.

Explanation:

In in equation like this, it is most useful to use a "multiplier," or the LCM of the two denominators of the two terms on the left side of the given equation. In other words, the first step to find the least common multiple of the two denominators, `2` and `4`.

As you will determine, the least common multiple or LCM of the numbers `2` and `4` is `4`. Now, the second step is to multiply both sides of the equation by the LCM, `4`.

`(3v-7)/2 + (v-9)/4 = 10`

`((3v-7) * 4)/2 + ((v-9)*4)/4 = 10*4`

`((3v-7) * 2)/1 + ((v-9)*1)/1 = 10*4`

`((3v-7) * 2) + (v-9) = 40`

From here, you continue solving, and "combine like-terms" to put all of the `v`-values on one side and numbers on the other.

`((3v-7) * 2) + (v-9) = 40`

`(6v-14)+(v-9)=40`

`7v-23=40`

`7v=63`

Now, we divide both sides of the equation by `7`, and we are left with `v=9`. Therefore, this is your answer.

I hope that helps!