Let's solve the given equation step by step.
The given equation is:
[tex]\[
\frac{4}{7} a - \frac{2}{3} = -\frac{1}{3}
\][/tex]
Step 1: Isolate the term with [tex]\( a \)[/tex] on one side
To isolate the term with [tex]\( a \)[/tex], we need to get rid of the constant term on the left side. We can do this by adding [tex]\(\frac{2}{3}\)[/tex] to both sides of the equation.
[tex]\[
\frac{4}{7} a - \frac{2}{3} + \frac{2}{3} = -\frac{1}{3} + \frac{2}{3}
\][/tex]
Simplifying the left side, we get:
[tex]\[
\frac{4}{7} a = -\frac{1}{3} + \frac{2}{3}
\][/tex]
Step 2: Simplify the right side
Now, we simplify the right side. Both fractions have the same denominator, so we can combine them easily:
[tex]\[
\frac{4}{7} a = \frac{2 - 1}{3} = \frac{1}{3}
\][/tex]
Step 3: Solve for [tex]\( a \)[/tex]
Now that we have isolated the term with [tex]\( a \)[/tex], we need to solve for [tex]\( a \)[/tex]. We do this by multiplying both sides by the reciprocal of [tex]\(\frac{4}{7}\)[/tex]. The reciprocal of [tex]\(\frac{4}{7}\)[/tex] is [tex]\(\frac{7}{4}\)[/tex].
[tex]\[
a = \frac{7}{4} \times \frac{1}{3}
\][/tex]
Step 4: Perform the multiplication
To multiply fractions, we multiply the numerators together and the denominators together:
[tex]\[
a = \frac{7 \times 1}{4 \times 3} = \frac{7}{12}
\][/tex]
So, the solution for [tex]\( a \)[/tex] is:
[tex]\[
a = \frac{7}{12}
\][/tex]
