# How do you solve 8x+15=3x-20?

May 9, 2018

$x = - 7$

#### Explanation:

show below

$8 x + 15 = 3 x - 20$

$8 x - 3 x = - 20 - 15$

$5 x = - 35$

$x = - 7$

May 9, 2018

The solution to the equation is $x = - 7$

#### Explanation:

Start by getting like terms on the same side of the equation, I'll subtract fifteen from both sides first:

$8 x + 15 = 3 x - 20$
$8 x = 3 x - 35$

Next, subtract $3 x$ from both sides:

$5 x = - 35$

And finally, divide by $5$ on both sides.

$\frac{\textcolor{red}{\cancel{5}} x}{\textcolor{red}{\cancel{5}}} = \frac{- 35}{5}$

The fives on the left cancel each other out (because $\frac{5 x}{5} = x$), leaving us with this:

$x = \frac{- 35}{5}$

$x = \textcolor{red}{- 7}$

May 9, 2018

Re-arrange the equation, and you will find that $x = - 7$

#### Explanation:

First, we'll add and subtract values from both sides such that all of the $x$-terms and their coefficients will end up on one side, and the constants will be on the other:

$8 x + 15 \textcolor{red}{- 3 x} = \cancel{3 x} - 20 \textcolor{red}{\cancel{- 3 x}}$

$8 x \textcolor{red}{- 3 x} + 15 = - 20$

$5 x + 15 = - 20$

$5 x \cancel{+ 15} \textcolor{red}{\cancel{- 15}} = - 20 \textcolor{red}{- 15}$

$5 x = - 20 \textcolor{red}{- 15}$

$5 x = - 35$

Now that the equation has been rearranged as we like it, we'll divide both sides by $x$'s coefficient. In this expression, the coefficient is 5:

$\frac{\cancel{5} x}{\textcolor{red}{\cancel{5}}} = \frac{- 35}{\textcolor{red}{5}}$

$x = \frac{- 35}{\textcolor{red}{5}}$

$\textcolor{g r e e n}{x = - 7}$