# How do you solve (x-3) /4 + x/2 =3?

Jun 3, 2016

$x = 5$

#### Explanation:

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

First, we remove the fractions by multiplying the equation by the LCM of $4$ and $2$, our two denominators:

LCM of $4$ and $2$ = $4$

Multiply the equation by $4$.

This means, the expression on the left side of the = sign will be multiplied by $4$ and the expression on the right side of the = sign will be multiplied by $4$:

$\left[\frac{x - 3}{4} + \frac{x}{2}\right] \textcolor{red}{\times 4} = 3 \textcolor{red}{\times 4}$

$\left[\frac{x - 3}{4} \textcolor{red}{\times 4}\right] + \left[\frac{x}{2} \textcolor{red}{\times 4}\right] = 12$

$\left[\frac{x - 3}{\cancel{4}} \times \cancel{4}\right] + \left[\frac{x}{\cancel{2}} \times {\cancel{4}}^{2}\right] = 12$

$x - 3 + \left(x \times 2\right) = 12$

$x - 3 + 2 x = 12$

$3 x - 3 = 12$

Next, add $3$ to both sides of the equation:

$3 x - 3 \textcolor{red}{+ 3} = 12 \textcolor{red}{+ 3}$

$3 x = 15$

Finally, divide both sides by $3$:

$\frac{3 x}{\textcolor{red}{3}} = \frac{15}{\textcolor{red}{3}}$

$x = 5$

You can check your answer by putting back the value $x = 5$ in the question:

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

Solving the left side:

$= \frac{5 - 3}{4} + \frac{5}{2}$

$= \frac{2}{4} + \frac{5}{2}$

$= \frac{1}{2} + \frac{5}{2}$

$= \frac{1 + 5}{2}$

$= \frac{6}{2} = \textcolor{red}{3}$

Jun 3, 2016

x = 5

#### Explanation:

To eliminate the fractions in this equation $\textcolor{b l u e}{\text{multiply all terms on both sides}}$ by the L.C.M. (lowest common multiple) of 2 and 4 which is 4.

$\Rightarrow \left[{\cancel{4}}^{1} \times \frac{x - 3}{\cancel{4}} ^ 1\right] + \left[{\cancel{4}}^{2} \times \frac{x}{\cancel{2}} ^ 1\right] = 4 \times 3$

The equation now simplifies to

x - 3 + 2x = 12

hence : 3x - 3 =12

and 3x = 15

divide both sides by 3

$\frac{{\cancel{3}}^{1} x}{\cancel{3}} ^ 1 = \frac{15}{3}$

$\Rightarrow x = 5 \text{ is the solution}$