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What is the solution to the equation [tex]$7c + 5 = 9(c - 3)$[/tex]?

A. [tex]$c = 2$[/tex]
B. [tex][tex]$c = 4$[/tex][/tex]
C. [tex]$c = 11$[/tex]
D. [tex]$c = 16$[/tex]


Sagot :

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]