# How do you solve 1/2+7x/10=13/20?

Jul 28, 2015

answer 1: color(blue)(x=-137/2
answer 2 :color(blue)(x=3/14

#### Explanation:

1. Assuming that $7 \left(\frac{x}{10}\right)$is a mixed fraction:
$\frac{1}{2} + 7 \left(\frac{x}{10}\right) = \frac{13}{20}$

Solving the mixed fraction:

$\frac{1}{2} + \frac{10 \cdot 7 + x}{10} = \frac{13}{20}$

$\frac{1}{2} + \frac{70 + x}{10} = \frac{13}{20}$

The L.C.M of the expression is $20$

$\frac{1 \cdot 10}{2 \cdot 10} + \frac{\left(70 + x\right) \cdot 2}{10 \cdot 2} = \frac{13}{20}$

$\frac{10}{\cancel{20}} + \frac{140 + 2 x}{\cancel{20}} = \frac{13}{\cancel{20}}$

$10 + 140 + 2 x = 13$

$2 x = 13 - 150$

answer 1: color(blue)(x=-137/2

1. Taking $7 \frac{x}{10}$ as a normal fraction:

$\frac{1}{2} + 7 \frac{x}{10} = \frac{13}{20}$

The L.C.M of the expression is $20$

$\frac{1 \cdot 10}{2 \cdot 10} + \frac{7 x \cdot 2}{10 \cdot 2} = \frac{13}{20}$

$\frac{10}{\cancel{20}} + \frac{14 x}{\cancel{20}} = \frac{13}{\cancel{20}}$

$10 + 14 x = 13$
$14 x = 3$
answer 2 :color(blue)(x=3/14