Question

Solve for bb. Express your answer as a proper or improper fraction in simplest terms.
minus, start fraction, 4, divided by, 7, end fraction, b, plus, start fraction, 3, divided by, 4, end fraction, equals, one half
−
7
4
​
b+
4
3
​
=
2
1
​

Answer 1

To solve the equation

\[
-\frac{4}{7}b + \frac{3}{4} = \frac{1}{2},
\]

we will isolate \( b \).

### Step 1: Move \(\frac{3}{4}\) to the other side of the equation.

Subtract \(\frac{3}{4}\) from both sides:

\[
-\frac{4}{7}b = \frac{1}{2} - \frac{3}{4}.
\]

### Step 2: Find a common denominator for the right side.

The common denominator for 2 and 4 is 4. Convert \(\frac{1}{2}\) to have a denominator of 4:

\[
\frac{1}{2} = \frac{2}{4}.
\]

Now we can rewrite the equation:

\[
-\frac{4}{7}b = \frac{2}{4} - \frac{3}{4}.
\]

### Step 3: Simplify the right side.

\[
\frac{2}{4} - \frac{3}{4} = \frac{2 - 3}{4} = \frac{-1}{4}.
\]

So the equation becomes:

\[
-\frac{4}{7}b = \frac{-1}{4}.
\]

### Step 4: Solve for \( b \).

To isolate \( b \), multiply both sides by \(-\frac{7}{4}\):

\[
b = \frac{-1}{4} \times -\frac{7}{4} = \frac{7}{16}.
\]

### Conclusion:

The solution for \( b \) is

\[
\boxed{\frac{7}{16}}.
\]