Question

-3(x-5)-2x=-10 solve for x

Answer 1

Answer:

x=5

Fast and loose:

Let's isolate -3(x-5)

$-3(x-5) = 2x-10\\-3(x-5) = 2(x-5)$

Now, if $x=5$, we get $-3(0) = 2(0)$ which is indeed true.  If $x\neq 5$, we can divide both sides by (x-5), and get $-3=2$ which is absurd. It means we have no more solutions.

Number crunching:

Let's distribute, bring all terms containging x to the LHS and the rest to the RHS:

$-3x+15-2x=-10\\-5x=-25\\x=\frac{-25}{-5} = 5$