Sure, let's solve the problem step-by-step.
We are given the following information:
1. When 12 times a certain number [tex]\( x \)[/tex] is divided by 7, the quotient is 6.
2. The remainder is 2 more than the original number [tex]\( x \)[/tex].
Let's denote:
- The number as [tex]\( x \)[/tex].
- The remainder as [tex]\( r \)[/tex].
According to the problem:
[tex]\[ 12x = 7q + r \][/tex]
Where [tex]\( q \)[/tex] is the quotient and [tex]\( r \)[/tex] is the remainder.
Given:
[tex]\[ q = 6 \][/tex]
[tex]\[ r = x + 2 \][/tex]
We substitute these values into the equation:
[tex]\[ 12x = 7 \cdot 6 + (x + 2) \][/tex]
Now, simplify the right-hand side:
[tex]\[ 12x = 42 + x + 2 \][/tex]
Combine the constants:
[tex]\[ 12x = 44 + x \][/tex]
Next, we solve for [tex]\( x \)[/tex] by isolating it on one side. Subtract [tex]\( x \)[/tex] from both sides:
[tex]\[ 12x - x = 44 \][/tex]
[tex]\[ 11x = 44 \][/tex]
Now, divide both sides by 11:
[tex]\[ x = \frac{44}{11} \][/tex]
[tex]\[ x = 4 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is 4.
So, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{4}\)[/tex].
