Sure, let's solve the equation step-by-step:
We start with the given equation:
[tex]\[ 7c + 5 = 9(c - 3) \][/tex]
First, distribute the 9 on the right side:
[tex]\[ 9(c - 3) = 9c - 27 \][/tex]
So, the equation becomes:
[tex]\[ 7c + 5 = 9c - 27 \][/tex]
Next, let's combine like terms by subtracting [tex]\(7c\)[/tex] from both sides:
[tex]\[ 7c + 5 - 7c = 9c - 27 - 7c \][/tex]
[tex]\[ 5 = 2c - 27 \][/tex]
Now, add 27 to both sides to isolate the term with [tex]\(c\)[/tex]:
[tex]\[ 5 + 27 = 2c - 27 + 27 \][/tex]
[tex]\[ 32 = 2c \][/tex]
Finally, divide both sides by 2 to solve for [tex]\(c\)[/tex]:
[tex]\[ \frac{32}{2} = \frac{2c}{2} \][/tex]
[tex]\[ c = 16 \][/tex]
So, the solution to the equation [tex]\(7c + 5 = 9(c - 3)\)[/tex] is:
[tex]\[ c = 16 \][/tex]
Thus, the correct answer is:
[tex]\[ c = 16 \][/tex]
