Certainly! Let's solve the equation step-by-step:
The given equation is:
[tex]\[ 5 - \frac{1}{6} x = \frac{13}{3} \][/tex]
Step 1: Isolate the term involving [tex]\( x \)[/tex].
We want to get all the [tex]\( x \)[/tex] terms on one side and the constants on the other side. So, let's subtract 5 from both sides of the equation:
[tex]\[ 5 - 5 - \frac{1}{6} x = \frac{13}{3} - 5 \][/tex]
[tex]\[ - \frac{1}{6} x = \frac{13}{3} - \frac{15}{3} \][/tex]
Notice that we represented 5 as [tex]\( \frac{15}{3} \)[/tex] to have a common denominator.
Step 2: Simplify the constants:
[tex]\[ - \frac{1}{6} x = \frac{13 - 15}{3} \][/tex]
[tex]\[ - \frac{1}{6} x = -\frac{2}{3} \][/tex]
Step 3: Solve for [tex]\( x \)[/tex].
To isolate [tex]\( x \)[/tex], multiply both sides of the equation by -6 (which is the reciprocal of -[tex]\(\frac{1}{6}\)[/tex]):
[tex]\[ x = -6 \left( -\frac{2}{3} \right) \][/tex]
Step 4: Simplify the multiplication:
[tex]\[ x = -6 \times -\frac{2}{3} \][/tex]
[tex]\[ x = 4 \][/tex]
So, the solution to the equation is:
[tex]\[ \boxed{4} \][/tex]
Therefore, the correct choice is:
A. The solution is [tex]\(\boxed{4}\)[/tex] (Type an integer or a simplified fraction.)
