Certainly! Let's work through the problem step-by-step to find the value of [tex]\( x \)[/tex] in terms of [tex]\( a \)[/tex].
Given the equation:
[tex]\[
\frac{3}{a} x - 4 = 20
\][/tex]
1. Isolate the term involving [tex]\( x \)[/tex]:
To do this, we'll add 4 to both sides of the equation:
[tex]\[
\frac{3}{a} x - 4 + 4 = 20 + 4
\][/tex]
Simplifying both sides:
[tex]\[
\frac{3}{a} x = 24
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
We need to isolate [tex]\( x \)[/tex] on one side. To do this, we'll multiply both sides of the equation by [tex]\( \frac{a}{3} \)[/tex] (which is the reciprocal of [tex]\( \frac{3}{a} \)[/tex]):
[tex]\[
\left(\frac{a}{3}\right) \cdot \frac{3}{a} x = 24 \cdot \left(\frac{a}{3}\right)
\][/tex]
Simplifying the left side:
[tex]\[
x = 24 \cdot \frac{a}{3}
\][/tex]
3. Simplify the expression:
[tex]\[
x = 24 \cdot \frac{a}{3} = 8a
\][/tex]
Thus, the value of [tex]\( x \)[/tex] in terms of [tex]\( a \)[/tex] is:
[tex]\[
x = 8a
\][/tex]
