Question

How do you solve `3/4+1/2x=2+1/4x`?

Answer 1

`x=5`

Explanation:

We have, `frac{3}4 + x/2=2+x/4`

On further simplification,we get,

`x/2-x/4=2-frac{3}4`

Or,`x/4=5/4`

Thus, `x` is equal to 5

Answer 2

5

Explanation:

In these cases, you always want to move terms with `x` to one side and numbers to the other. So, moving things around, we get

`1/2x-1/4x=2-3/4`

(remember to change signs when you move things to the opposite side!)

Simplifying that, we get

`2/4x-1/4x=8/4-3/4`

`1/4x=5/4`

Multiplying both sides by 4, we get

`x=5`

and voila!

Answer 3

`x=5`

Explanation:

`3/4+1/2x=2+1/4x`

If you have an equation which has fractions, you can get rid of the denominators by multiplying by the LCM of the denominators.

(In this case it is `4`)

`(color(blue)(cancel4xx)3)/cancel4+(color(blue)(cancel4^2xx)1x)/cancel2=color(blue)(4xx)2+(color(blue)(cancel4xx)1x)/cancel4`

`3 +2x=8+x" "larr` no fractions !

`2x-x = 8-3`

`x=5`