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# How do you solve (X+3)/(2) -(X-4)/(7) = 1?

Jan 19, 2017

See the entire solution process below.

#### Explanation:

First, multiply each side of the equation by the lowest common denominator for both fractions, $\textcolor{red}{14}$, to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{14} \left(\frac{X + 3}{2} - \frac{X - 4}{7}\right) = \textcolor{red}{14} \times 1$

$\left(\textcolor{red}{14} \times \frac{X + 3}{2}\right) - \left(\textcolor{red}{14} \times \frac{X - 4}{7}\right) = 14$

$\left(\cancel{\textcolor{red}{14}} 7 \times \frac{\left(X + 3\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right) - \left(\cancel{\textcolor{red}{14}} 2 \times \frac{\left(X - 4\right)}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}}\right) = 14$

$7 \left(X + 3\right) - 2 \left(X - 4\right) = 14$

$7 X + 21 - 2 X + 8 = 14$

$5 X + 29 = 14$

$5 X + 29 - \textcolor{red}{29} = 14 - \textcolor{red}{29}$

$5 X + 0 = - 15$

$5 X = - 15$

$\frac{5 X}{\textcolor{red}{5}} = - \frac{15}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} X}{\cancel{\textcolor{red}{5}}} = - 3$

$X = - 3$

Jan 20, 2017

$x = - 3$

#### Explanation:

Making the denominators all the same.

$\text{ "color(green)([ (x+3)/2color(red)(xx1)]" " -" } \left[\frac{x - 4}{7} \textcolor{red}{\times 1}\right] = \left[1 \textcolor{red}{\times 1}\right]$

" "color(green)([ (x+3)/2color(red)(xx7/7)]color(white)(..) -color(white)(.)[(x-4)/7color(red)(xx2/2)]=[1color(red)(xx14/14)]

$\text{ "color(green)([ (7x+21)/14]" "color(white)(.) -color(white)(...)[(2x-8)/14]" "=" } \left[\frac{14}{14}\right]$

Multiply everything by 14

$\text{ } \textcolor{g r e e n}{7 x \textcolor{red}{+ 21} - 2 x \textcolor{red}{+ 8} = 14}$

$\text{ } \textcolor{g r e e n}{7 x - 2 x \textcolor{red}{+ 21 + 8} = 14} \leftarrow$ Regrouped

$\text{ } 5 x + 29 = 14$

Subtract 29 from both sides

$\text{ } 5 x = - 15$

Divide both sides by 5

$\text{ } x = - 3$

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