Question

How do you solve `55x-3(9x+12)= -64`?

Answer 1

`x=-1`

Explanation:

Let's start by distributing the `-3` to the terms in parenthesis. Here, we are just multiplying, and we get:

`55x-27x-36=-64`

We can simplify the terms on the left to get:

`28x-36=-64`

Next, add `36` to both sides to get:

`28x=-28`

Divide both sides by `28` to get:

`x=-1`

Hope this helps!

Answer 2

Expand the terms in the parentheses and then you can solve for `x`, which should be `x=-1`

Explanation:

First, let's expand the parentheses. We'll do this by distributing the multiplication factor that's outside the parentheses to all terms inside of them. We'll do this in two steps.

First, let's distribute the 3-times multiplier:

`55x-3(9x+12)=-64 rArr 55x-(3*9x+3*12)=-64`

`55x-(27x+36)=-64`

Next, let's treat the minus sign as a -1 multiplier. This will eliminate the need for the parentheses altogether, since we've now distributed everything:

`55x-(27x+36)=55x+(-1)(27x+36)=-64`

`55x+(-27x-36)=55x-27x-36=-64`

Now, we combine like terms. We'll combine the `x` terms first, and then the constants by adding 36 to both sides, effectively moving it to the right hand side:

`55x-27x=(55-27)x=28x rArr 28x-36=-64`

`28x-cancel(36)+cancel(36)=-64+36`

`28x=-28`

Finally, we divide through by `x`'s coefficient to get our answer:

`28/28x=(-28)/28`

`color(red)(x=-1)`