Question

How do you solve `-4( 5+ 8n ) - ( 5n - 4) = 1- 3n - 5n`?

Answer 1

First, simplify the equation, then perform the same operations on both sides to isolate `n` which gives `n = - 17/29`

Explanation:

The first thing we should think of is how to simplify the equation. We notice that there are parentheses and multiplications which can be performed on the left-hand-side of the equation. Let's start there and see where we can get. We'll begin by looking at the multiplications outside the parentheses:

`\color{red}((-4)) * (5+8n) + \color{blue}((-1)) * (5n-4) = 1 - 3n - 5n`

Note that the multiplication of the first parenthesis is clearly by a negative value, while the second is not so obvious, so we can make it clear by multiplying by `-1`. Finishing the multiplication we get:

`\color{red}(-20-32n) + \color{blue}(-5n+4) = 1 - 3n - 5n`

now we can gather terms of the same type on each side:

`\color{magenta}(-32n-5n) + \color{green}(-20+4) = 1 \color{orange}(-3n - 5n)`

adding like terms together we get:

`\color{magenta}(-37n) + \color{green}(-16) = 1 \color{orange}(-8n)`

this is as simple as we can get each side. To solve this equation we need to isolate our variable, `n`, on one side by doing operations on both sides of the equation. We can start by getting rid of the `\color{green}(-16)` on the left hand side by adding `16` to both sides:

`\color{magenta}(-37n) + \color{green}(-16) +16 = 1 +16 \color{orange}(-8n)`

`\color{magenta}(-37n) = 17 \color{orange}(-8n)`

Next, we can get rid of the `\color{orange}(-8n)` on the right hand side by adding `8n` to both sides:

`\color{magenta}(-37n) +8n= 17 \color{orange}(-8n) +8n`

`\color{magenta}(-29n) = 17`

finally, we can divide each side of the equation by `-29`:

`\color{magenta}(-29n)/-29 = 17/-29`

`n = - 17/29`