To solve the equation [tex]\( 7c + 5 = 9(c - 3) \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[ 7c + 5 = 9(c - 3) \][/tex]
2. Distribute the 9 on the right side of the equation:
[tex]\[ 7c + 5 = 9c - 27 \][/tex]
3. To isolate the variable [tex]\( c \)[/tex], you must first move all terms involving [tex]\( c \)[/tex] to one side of the equation and constant terms to the other. Subtract [tex]\( 9c \)[/tex] from both sides:
[tex]\[ 7c - 9c + 5 = -27 \][/tex]
Simplify the left side:
[tex]\[ -2c + 5 = -27 \][/tex]
4. Next, move the constant term on the left side to the right side by subtracting 5 from both sides:
[tex]\[ -2c = -27 - 5 \][/tex]
Simplify the right side:
[tex]\[ -2c = -32 \][/tex]
5. Finally, solve for [tex]\( c \)[/tex] by dividing both sides of the equation by -2:
[tex]\[ c = \frac{-32}{-2} \][/tex]
Simplify the division:
[tex]\[ c = 16 \][/tex]
So the 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].
