Question

Please help, I will give a medal :)



Solve 9c + 4 = -23.

Answer 1

9c=-27
c=-27/9
c=-3

Answer 2

9c=-23-4
9c=-27
c=-27/9
c=-3

forgot one step

Answer 3

\[9c+4=-23\]
We have to begin by recognizing the problem we have in front of us, we see a equality, and a letter, often called a "variable", that means that it's a number, but changes depending of the value we give it.
in this case, we only see one "c" and that is what we call a "single variable equation" or more like "1st grade equation".
traducing it, in verbal language:
"That number, multiplied by 9 and added 4 gives me a result of -23?"
easy, huh?
To find that number we have to play with the equation and some axioms, let's begin:
\[9x+4=-23\]
now, you may have notices in your algebra classes that we have to leave the variables in one side of the equality and the constants(numbers without variable) on the other side.
To do that, I'll substract 4 on the left side on the equality, but to keep it balanced, I'll have to do it on the other side as well:
\[9c+4-4=-23-4\]
we know that 4-4=0 and that negative numbers stay negatibe and they sum, so let's simplify what we just did:
\[9c=-27\]
I want to leave the "c" alone on the left side of the equality, but in order to do that I'll have to divide both sides by 9:
\[\frac{ 9c }{ 9 }=\frac{ -27 }{ 9 }\]
we know that 9/9 is equal to 1 and 27/9 is equal to 3, but it's negative so we have to put a negative sign:
\[c=\frac{ -27 }{ 9 }=-3\]
so we conclude that:
\[c=-3\]
and we can even verify it, by replacing it on the original equation:
\[9(-3)+4=-23\]
\[-27+4=-23\]
\[-23=-23\]
That last step was a verification to see if the calue I got for "c" was correct, and it was.
So with the calm of our heart we can say that the problem is solved.