Certainly! Let's solve the equation step-by-step:
We start with the given equation:
[tex]\[ 7c + 5 = 9(c - 3) \][/tex]
First, we distribute the 9 on the right-hand side to eliminate the parentheses:
[tex]\[ 7c + 5 = 9c - 27 \][/tex]
Next, we need to gather all the terms containing [tex]\( c \)[/tex] on one side and the constant terms on the other side. We do this by subtracting [tex]\( 9c \)[/tex] from both sides of the equation:
[tex]\[ 7c + 5 - 9c = 9c - 27 - 9c \][/tex]
[tex]\[ 7c - 9c + 5 = -27 \][/tex]
[tex]\[ -2c + 5 = -27 \][/tex]
Now, we isolate the term containing [tex]\( c \)[/tex] by subtracting 5 from both sides:
[tex]\[ -2c + 5 - 5 = -27 - 5 \][/tex]
[tex]\[ -2c = -32 \][/tex]
Next, we solve for [tex]\( c \)[/tex] by dividing both sides of the equation by -2:
[tex]\[ c = \frac{-32}{-2} \][/tex]
[tex]\[ c = 16 \][/tex]
So, the correct solution to the equation [tex]\( 7c + 5 = 9(c - 3) \)[/tex] is:
[tex]\[ c = 16 \][/tex]
Therefore, the correct answer is:
[tex]\[ c = 16 \][/tex]
