Sure, let's solve the equation step by step.
The given equation is:
[tex]\[
-8c + 13 = -10c - 9
\][/tex]
### Step 1: Move all terms involving [tex]\(c\)[/tex] to one side of the equation
To do this, let's add [tex]\(10c\)[/tex] to both sides to move all [tex]\(c\)[/tex]-terms to the left side:
[tex]\[
-8c + 10c + 13 = -9
\][/tex]
### Step 2: Simplify the equation
Combine the [tex]\(c\)[/tex]-terms on the left side:
[tex]\[
2c + 13 = -9
\][/tex]
### Step 3: Move the constant term to the other side of the equation
To isolate the [tex]\(c\)[/tex]-term, subtract 13 from both sides:
[tex]\[
2c + 13 - 13 = -9 - 13
\][/tex]
[tex]\[
2c = -22
\][/tex]
### Step 4: Solve for [tex]\(c\)[/tex]
Divide both sides of the equation by 2 to solve for [tex]\(c\)[/tex]:
[tex]\[
c = \frac{-22}{2}
\][/tex]
[tex]\[
c = -11
\][/tex]
So, the solution to the equation is:
[tex]\[
c = -11
\][/tex]
Thus, the correct option is [tex]\(c = -11\)[/tex].
