Simplify 5/14a+−2/5c+1/8b−2/5c+3/8b+7/14

To simplify the expression \( \frac{5}{14}a - \frac{2}{5}c + \frac{1}{8}b - \frac{2}{5}c + \frac{3}{8}b + \frac{7}{14} \), we will first combine like terms.

### Step 1: Combine the like terms involving \( c \)
- The \( c \) terms are \( -\frac{2}{5}c - \frac{2}{5}c \):
\[
-\frac{2}{5}c - \frac{2}{5}c = -\frac{4}{5}c
\]

### Step 2: Combine the like terms involving \( b \)
- The \( b \) terms are \( \frac{1}{8}b + \frac{3}{8}b \):
\[
\frac{1}{8}b + \frac{3}{8}b = \frac{4}{8}b = \frac{1}{2}b
\]

### Step 3: Combine the constant terms
- The constant terms are \( \frac{7}{14} \), which simplifies to \( \frac{1}{2} \):
\[
\frac{7}{14} = \frac{1}{2}
\]

### Step 4: Write the simplified expression
Now we can combine all the simplified parts:
\[
\frac{5}{14}a - \frac{4}{5}c + \frac{1}{2}b + \frac{1}{2}
\]

### Final simplified expression
The final simplified expression is:
\[
\frac{5}{14}a - \frac{4}{5}c + \frac{1}{2}b + \frac{1}{2}
\]