Question

How many Solutions are there for -6(3x+2)=2x-5-20x-7

Answer 1

First of all, expand the left hand side:

$-18x-12 = 2x-5-20x-7$

Sum like terms on the right hand side:

$-18x-12 = -18x-12$

As you can see, the equation turned to be an identity: it doesn't matter which value for x you are choosing: you're evaluating the same expression in both sides, so they will always be the same.

In other words, you're asking: which value for x should I choose so that -18x-12 and -18x-12 evaluate to the same number? Well, obvisouly any value for x will do.

So, there are infinitely many solutions to this equation, namely ever real number is a solution of this equation.