How do you solve -4/5x+6=x-3?

May 23, 2018

Re-arrange the equation, and divide through by $x$'s coefficient to find $x = 5$

Explanation:

First, we'll re-arrange the equation such that all constants are on one side, and all of the $x$-related terms are on the other. We'll do this by adding and subtracting terms from both sides so terms will cancel out on one side, but modify the other:

First, we'll move the $\frac{4}{5} x$ term:

$\cancel{- \frac{4}{5} x} + 6 \textcolor{red}{\cancel{+ \frac{4}{5} x}} = x - 3 \textcolor{red}{+ \frac{4}{5} x}$

$6 = x \left(1 + \textcolor{red}{\frac{4}{5}}\right) - 3$

$6 = \frac{9}{5} x - 3$

Next, we'll move the -3 constant to the left-hand side:

$6 \textcolor{b l u e}{+ 3} = \frac{9}{5} x \cancel{- 3} \textcolor{b l u e}{\cancel{+ 3}}$

$9 = \frac{9}{5} x$

Now, all that's left is to divide both sides by $x$'s coefficient. Because we're dividing a fraction, we can write it as both sides being multiplied by its inverse:

$\cancel{9} \textcolor{red}{\times \frac{5}{\cancel{9}}} = \cancel{\frac{9}{5}} x \times \textcolor{red}{\cancel{\frac{5}{9}}}$

$\textcolor{g r e e n}{x = 5}$