# How do you simplify? 5x+1(x+5+15) = x+5(5x+1+35)

$x = - 8$

#### Explanation:

We have:

$5 x + 1 \left(x + 5 + 15\right) = x + 5 \left(5 x + 1 + 35\right)$

One way we can simplify this is to work through the Order of Operations:

• $\textcolor{red}{P}$ - Parentheses (also known as Brackets)
• $\textcolor{b l u e}{E}$ - Exponents
• $\textcolor{g r e e n}{M}$ - Multiplication
• $\textcolor{g r e e n}{D}$ - Division (this has the same weight as M and so I gave it the same colour)
• $\textcolor{b r o w n}{A}$ - Addition
• $\textcolor{b r o w n}{S}$ - Subtraction - again, same weight as A and so the same colour)

Our question has $\textcolor{red}{P}$, so let's simplify those first:

$5 x + 1 \left(x + 20\right) = x + 5 \left(5 x + 36\right)$

We've taken $\textcolor{red}{P}$ as far as possible, so let's do $\textcolor{g r e e n}{M}$ - by doing the distributions:

$5 x + x + 20 = x + 25 x + 180$

And now $\textcolor{b r o w n}{A}$

$6 x + 20 = 26 x + 180$

We've simplified the expression, so now we need a bit of algebra. Let's move terms so we have $x$ terms on one side and non-$x$ terms on the other:

$6 x \textcolor{red}{- 26 x - 20} + 20 = 26 x \textcolor{red}{- 26 x - 20} + 180$

$- 20 x = 160$

$x = \frac{160}{- 20} = - 8$

$5 \left(- 8\right) + 1 \left(\left(- 8\right) + 5 + 15\right) = \left(- 8\right) + 5 \left(5 \left(- 8\right) + 1 + 35\right)$

$- 40 + 1 \left(12\right) = \left(- 8\right) + 5 \left(- 40 + 36\right)$

$- 28 = \left(- 8\right) + 5 \left(- 4\right)$

$- 28 = \left(- 8\right) - 20$

-28=-28color(white)(000)color(green)sqrt

~~~~~~~~~~

We could also have done this:

$5 x + 1 \left(x + 5 + 15\right) = x + 5 \left(5 x + 1 + 35\right)$

distribute first:

$5 x + x + 5 + 15 = x + 25 x + 5 + 175$

then combine like terms:

$6 x + 20 = 26 x + 180$

and then solve in the normal way.