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

May 29, 2018

$x = 5$

#### Explanation:

We have, $\frac{3}{4} + \frac{x}{2} = 2 + \frac{x}{4}$

On further simplification,we get,

$\frac{x}{2} - \frac{x}{4} = 2 - \frac{3}{4}$

Or,$\frac{x}{4} = \frac{5}{4}$

Thus, $x$ is equal to 5

May 29, 2018

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

$\frac{1}{2} x - \frac{1}{4} x = 2 - \frac{3}{4}$

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

Simplifying that, we get

$\frac{2}{4} x - \frac{1}{4} x = \frac{8}{4} - \frac{3}{4}$

$\frac{1}{4} x = \frac{5}{4}$

Multiplying both sides by 4, we get

$x = 5$

and voila!

May 29, 2018

$x = 5$

#### Explanation:

$\frac{3}{4} + \frac{1}{2} x = 2 + \frac{1}{4} x$

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 $4$)

$\frac{\textcolor{b l u e}{\cancel{4} \times} 3}{\cancel{4}} + \frac{\textcolor{b l u e}{{\cancel{4}}^{2} \times} 1 x}{\cancel{2}} = \textcolor{b l u e}{4 \times} 2 + \frac{\textcolor{b l u e}{\cancel{4} \times} 1 x}{\cancel{4}}$

$3 + 2 x = 8 + x \text{ } \leftarrow$ no fractions !

$2 x - x = 8 - 3$

$x = 5$