# How do you solve 3/7x+1/2=3 by clearing the fractions?

Sep 30, 2017

$x = \frac{35}{6}$

#### Explanation:

$\frac{3}{7} x + \frac{1}{2} = 3$

$\frac{3}{7} x = 3 - \frac{1}{2}$ isolate terms with variable
$\frac{3}{7} x = \setminus \textcolor{c r i m s o n}{\frac{6}{2}} - \frac{1}{2}$ common denominator on right side
$\frac{3}{7} x = \frac{5}{2}$ simplify

$\frac{3}{7} x \left(\setminus \textcolor{t e a l}{\frac{2}{2}}\right) = \frac{5}{2} \left(\setminus \textcolor{t e a l}{\frac{7}{7}}\right)$ multiply to get common denominator overall
$\setminus \textcolor{s e a g r e e n}{\frac{6}{14}} x = \setminus \textcolor{s e a g r e e n}{\frac{35}{14}}$

$x = \setminus \textcolor{\in \mathrm{di} g o}{\frac{35}{14} \cdot \frac{14}{6}}$ divide (multiply by reciprocal for fractions) to get variable
$x = \frac{35}{6}$

Sep 30, 2017

color(blue)(x=35/6 or color(blue)(5 5/6

#### Explanation:

$\frac{3}{7} x + \frac{1}{2} = 3$

$\therefore \frac{6 x + 7}{14} = \frac{42}{14}$

multiply both sides by $14$

$\therefore 6 x + 7 = 42$

$\therefore 6 x = 42 - 7$

$\therefore 6 x = 35$

:.color(blue)(x=35/6 or color(blue)( 5 5/6

~~~~~~~~~~~~~~~~~~~~

check:-

$\therefore \frac{3}{7} \left(\textcolor{b l u e}{\frac{35}{6}}\right) + \frac{1}{2} = 3$

$\therefore \frac{\cancel{3}}{\cancel{7}} ^ \textcolor{b l u e}{1} \times {\cancel{35}}^{\textcolor{b l u e}{5}} / {\cancel{6}}^{\textcolor{b l u e}{2}} + \frac{1}{2} = 3$

$\therefore \frac{5}{2} + \frac{1}{2} = 3$

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

:.color(blue)(3=3

Sep 30, 2017

$x = 5 \frac{5}{6}$

#### Explanation:

When you have an EQUATION with fractions, you can get rid of the denominators immediately by multiplying through by the LCM of the denominators to cancel them.

$\frac{3}{7} x + \frac{1}{2} = 3 \text{ } \left(L C D = \textcolor{b l u e}{14}\right)$

$\frac{\textcolor{b l u e}{14} \times 3 x}{7} + \frac{\textcolor{b l u e}{14} \times 1}{2} = \textcolor{b l u e}{14} \times 3 \text{ } \left(\leftarrow \times \textcolor{b l u e}{14}\right)$

$\frac{\textcolor{b l u e}{{\cancel{14}}^{2}} \times 3 x}{\cancel{7}} + \frac{\textcolor{b l u e}{{\cancel{14}}^{7}} \times 1}{\cancel{2}} = \textcolor{b l u e}{14} \times 3 \text{ } \leftarrow$ cancel denominators

$6 x + 7 = 42 \text{ } \leftarrow$ no fractions!

$6 x = 35$

$x = \frac{35}{6}$

$x = 5 \frac{5}{6}$