Let's solve the equation [tex]\(\frac{a}{b} \cdot x = a\)[/tex] for [tex]\(x\)[/tex].
1. Start with the given equation:
[tex]\[
\frac{a}{b} \cdot x = a
\][/tex]
2. Isolate [tex]\(x\)[/tex]:
To isolate [tex]\(x\)[/tex], we need to eliminate the fraction [tex]\(\frac{a}{b}\)[/tex]. To do this, multiply both sides of the equation by the reciprocal of [tex]\(\frac{a}{b}\)[/tex], which is [tex]\(\frac{b}{a}\)[/tex]:
[tex]\[
\frac{b}{a} \cdot \frac{a}{b} \cdot x = \frac{b}{a} \cdot a
\][/tex]
3. Simplify both sides:
On the left side, the [tex]\(\frac{b}{a}\)[/tex] and [tex]\(\frac{a}{b}\)[/tex] terms will cancel out, leaving:
[tex]\[
x = \frac{b}{a} \cdot a
\][/tex]
On the right side, [tex]\(a\)[/tex] terms cancel out:
[tex]\[
x = b
\][/tex]
4. Substitute the given values:
According to the information provided, [tex]\(a = b = 2\)[/tex]:
[tex]\[
x = 2
\][/tex]
Thus, the value of [tex]\(x\)[/tex] is [tex]\(2\)[/tex].
