To solve for [tex]\( x \)[/tex] in the given equation:
[tex]\[
\frac{1}{2} \cdot 4 = \frac{1}{3} \cdot x
\][/tex]
follow these steps:
1. Simplify the left-hand side of the equation:
[tex]\[
\frac{1}{2} \cdot 4 = \frac{4}{2} = 2
\][/tex]
So the equation becomes:
[tex]\[
2 = \frac{1}{3} \cdot x
\][/tex]
2. Isolate [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to get [tex]\( x \)[/tex] by itself on one side of the equation. We do this by multiplying both sides by the reciprocal of [tex]\(\frac{1}{3}\)[/tex], which is 3:
[tex]\[
2 \cdot 3 = x
\][/tex]
3. Solve:
[tex]\[
6 = x
\][/tex]
So, [tex]\( x = 6 \)[/tex].
4. Express as a mixed fraction:
Since 6 is a whole number, it can be expressed as a mixed fraction as:
[tex]\[
6 = 6 \frac{0}{1}
\][/tex]
This is because there is no fractional part; it's purely an integer.
Therefore, the solution is:
[tex]\[
x = 6 \frac{0}{1}
\][/tex]
or simply [tex]\( x = 6 \)[/tex].
