Question

How do you solve `-10(x+5)+76= -12`?

Answer 1

`x=3.8`

Explanation:

Multiplying out the brackets gives:

Don't forget you are multiplying by negative 10.

`-10x-50+76=-12`

`-10x+26=-12`

Subtract `color(blue)(26)` from both sides

`color(brown)(-10x+26color(blue)(-26)=-12color(blue)(-26))`

`-10x+0=-38`

Multiply both side by (-1) giving

`10x=38`

Divide both sides by 10

`10/10xx x= 38/10`

But `10/10 = 1`

`1xx x = 3.8`

`x=3.8`

'~~~~~~~~~ Check ~~~~~~~~~~~~~~~~
`color(brown)(-10(color(blue)(x)+5)+76=-12 -> -10(color(blue)(3.8)+5)+76=-12)`

Consider the left hand side only

`-38-50+76 -> -12`

`=> LHS=RHS" "-> x=3.8" confirmed"`

Answer 2

RESULT: 3.8
Maybe this one will be a little bit easier on the steps.

Explanation:

`-10(x+5)+76=-12`

Get rid of brackets by multiplying the coefficient with the digits in the brackets.

`-10x-50+76=-12`
`-10x+26=-12`

Unknowns: one side, knowns: another.

`-10x=-12-26`
`-10x=-38`
Since the both sides are negative, let's multiply them by `(-1)` to get rid of a negative sign.

`-10x =-38 |(-1)`
`10x=38`

Now, do just a division:
`x=38/10`
`x=3.8`