Answered

Solve the equation.
[tex]\[ 9(x+4) + 6 = 9x + 8 \][/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice:

A. The solution is [tex]\(\boxed{7}\)[/tex].
(Simplify your answer.)

B. The solution is all real numbers.

C. There is no solution.



Answer :

GinnyAnswer
To solve the equation [tex]\( 9(x + 4) + 6 = 9x + 8 \)[/tex], we need to simplify both sides and find the value of [tex]\( x \)[/tex].

First, distribute the 9 on the left side:
[tex]\[ 9(x + 4) + 6 = 9x + 36 + 6 \][/tex]
This simplifies to:
[tex]\[ 9x + 36 + 6 = 9x + 42 \][/tex]

Now, our equation looks like:
[tex]\[ 9x + 42 = 9x + 8 \][/tex]

Next, subtract [tex]\( 9x \)[/tex] from both sides of the equation:
[tex]\[ 9x + 42 - 9x = 9x + 8 - 9x \][/tex]
This simplifies to:
[tex]\[ 42 = 8 \][/tex]

Since 42 does not equal 8, we have a contradiction. Therefore, there is no value of [tex]\( x \)[/tex] that can satisfy the original equation.

Thus, the correct choice is:

C. There is no solution.