Question

Solve for bb. Express your answer as a proper or improper fraction in simplest terms.
start fraction, 2, divided by, 3, end fraction, equals, one third, minus, start fraction, 7, divided by, 10, end fraction, b
3
2
​
=
3
1
​
−
10
7
​
b

Answer 1

To solve the equation

\[
\frac{2}{3} = \frac{1}{3} - \frac{7}{10}b,
\]

we can start by isolating the term with \( b \). First, let's rearrange the equation:

\[
\frac{7}{10}b = \frac{1}{3} - \frac{2}{3}.
\]

Now, simplify the right side:

\[
\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}.
\]

So, the equation now is:

\[
\frac{7}{10}b = -\frac{1}{3}.
\]

Next, to solve for \( b \), we can multiply both sides by the reciprocal of \( \frac{7}{10} \), which is \( \frac{10}{7} \):

\[
b = -\frac{1}{3} \cdot \frac{10}{7}.
\]

Now, calculate the right side:

\[
b = -\frac{10}{21}.
\]

Thus, the solution for \( b \) is

\[
\boxed{-\frac{10}{21}}.
\]