Question

How do you solve `-3( x + 5) = x - 9+ 2( 5x + 2)`?

Answer 1

`x=-5/7`

Explanation:

First, we will look at the left side, which is `-3(x+5)`
We will distribute parentheses/brackets with this:

`x(y+z)=xy+xz`
Therefore, `-3(x+5)` is the same as `-3*xcancel(+)-3*5`

`-3*5=-15` so the equation will now be `-3x-15`.

Let's focus on the right side now.

`x-9+2(5x+2)`

We'll do the same thing as above, distribute parentheses using:
`x(y+z)=xy+xz`.

Therefore, `2(5x+2)=2*5x+2*2` which is the same as `10x+4`
Now, we put back the `x-9+`

Equation now:
`x-9+10x+4`
We first group like terms:
`x+10x+4-9`
Then add:
`11x+4-9`
Then subtract:
`11x-5`

Now we put both sides together to get
`-3x-15=11x-5`

Add `15` to both sides:
`-3x-15color(blue)+color(blue)15=11x-5color(blue)+color(blue)15`
Simplify:
`-3x=11x+10`

Subtract `11x` from both sides:
`-3xcolor(blue)-color(blue)11color(blue)x=11x+10color(blue)-color(blue)11color(blue)x`

Simplify:
`-14x=10`

Divide both sides by `-14`

`(-14x)/(-14)=10/-14`

to get:

`x=-5/7`