Question

How do you solve `-4(x-8)+(-x-3)=4`?

Answer 1

`x=5`

Explanation:

Lets simplify this equation first by distributing the `-4` to `(x-8)`

`-4(x-8)->-4x+32`

Now lets combine like terms:
`color(blue)(-4x)+color(red)32color(blue)(-x)color(red)(-3)=color(red)4 ->color(blue)(-5x)+color(red)29=color(red)4`

Now we'll isolate the `x` by first subtracting 29 from both sides:

`color(blue)(-5x)+color(red)cancel(29-29)=color(red)(4-29)`

`color(blue)(-5x)=color(red)(-25)`

Then divide `5` on both sides:
`color(blue)cancel(-5/5x)=color(red)(-25/5)`

`color(blue)x=color(red)5`

We can verify the solution but substituting `5` for `x` in the original equation.

`-4((color(red)5)-8)-(color(red)5)-3=4`

`-4(-3)-(color(red)5)-3=4`

`12-(color(red)5)-3=4`

`7-3=4`

`4=4`

Answer 2

`x=5`

Explanation:

Solve:

`-4(x-8)+(-x-3)=4`

Expand.

`-4x+32+(-x-3)=4`

Remove the parentheses.

`-4x+32-x-3=4`

Gather like terms.

`-4x-x+32-3=4`

Simplify.

`-5x+29=4`

Subtract `29` from both sides.

`-5x+cancel(29)-cancel(29)=4-29`

`-5x=-25`

Divide both sides by `-5`.

`(cancel(-5)x)/cancel(-5)=cancel(-25)^5/cancel(-5)^1`

`x=5`