To solve the equation
[tex]\[
\frac{7}{6a} + \frac{7}{2a} = 1
\][/tex]
we need to find the value of [tex]\( a \)[/tex]. Let's go through the solution step-by-step.
1. Combine the fractions: Notice that both terms on the left-hand side of the equation have [tex]\( a \)[/tex] in the denominator. To combine them, find a common denominator.
[tex]\[
\frac{7}{6a} + \frac{7}{2a} = 1
\][/tex]
The common denominator for [tex]\( 6a \)[/tex] and [tex]\( 2a \)[/tex] is [tex]\( 6a \)[/tex]. Rewrite the fractions with this common denominator:
[tex]\[
\frac{7}{6a} + \frac{7 \cdot 3}{2a \cdot 3} = \frac{7}{6a} + \frac{21}{6a}
\][/tex]
2. Add the fractions:
[tex]\[
\frac{7 + 21}{6a} = \frac{28}{6a}
\][/tex]
3. Simplify the fraction:
[tex]\[
\frac{28}{6a} = \frac{14}{3a}
\][/tex]
Therefore, our equation now looks like:
[tex]\[
\frac{14}{3a} = 1
\][/tex]
4. Solve for [tex]\( a \)[/tex]: To isolate [tex]\( a \)[/tex], multiply both sides of the equation by [tex]\( 3a \)[/tex]:
[tex]\[
14 = 3a
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{14}{3}
\][/tex]
Thus, the solution to the equation is:
[tex]\[
a = \frac{14}{3}
\][/tex]
If there were multiple solutions, they would all be listed, but in this case, there is only one solution. Hence, the value of [tex]\( a \)[/tex] is
[tex]\[
a = \frac{14}{3}
\][/tex]
