# How do you solve (5x)/2 - x = x/14 + 9/7?

Mar 25, 2018

$x = \frac{9}{10}$

#### Explanation:

$\frac{5 x}{2} - x = \frac{x}{14} + \frac{9}{7}$

Let's get a common denominator for the left side of the equation

$\frac{5 x}{2} - x \times \frac{2}{2} = \frac{x}{14} + \frac{9}{7}$

$\frac{5 x - 2 x}{2} = \frac{x}{14} + \frac{9}{7}$

$\frac{3 x}{2} = \frac{x}{14} + \frac{9}{7}$

Let's get all the $x$s on the same side

$\frac{3 x}{2} - \frac{x}{14} = \frac{9}{7}$

Common denominator

$\frac{7}{7} \times \frac{3 x}{2} - \frac{x}{14} = \frac{9}{7}$

$\frac{21 x}{14} - \frac{x}{14} = \frac{9}{7}$

Let's get another common denominator (we don't technically need this, but it makes the math easier later)

$\frac{20 x}{14} = \frac{9}{7} \times \frac{2}{2}$

$\frac{20 x}{14} = \frac{18}{14}$

Multiply both sides by $14$

$20 x = 18$

Divide by $20$ on both sides

$x = \frac{18}{20}$

$x = \frac{9}{10}$

Mar 25, 2018

$x = \frac{9}{10}$

#### Explanation:

We have an equation which has fractions.

$\frac{5 x}{2} - x = \frac{x}{14} + \frac{9}{7}$

We can get rid of the fractions immediately by multiplying the whole equation by the LCM of the denominators, which is $14$

$\frac{\textcolor{b l u e}{{\cancel{14}}^{7} \times} 5 x}{\cancel{2}} - \textcolor{b l u e}{14 \times} x = \frac{\textcolor{b l u e}{\cancel{14} \times} x}{\cancel{14}} + \frac{\textcolor{b l u e}{{\cancel{14}}^{2} \times} 9}{\cancel{7}} \text{ } \leftarrow$ cancel

$\text{ } 35 x - 14 x = x + 18$

$35 x - 14 x - x = 18$

$\textcolor{w h i t e}{\times \times \times \times} 20 x = 18$

$\textcolor{w h i t e}{\times \times \times \times x} x = \frac{18}{20}$

$\textcolor{w h i t e}{\times \times \times \times x} x = \frac{9}{10}$