What is the value of c?

To solve the equation \( 13c - 22 = -17c + 14 \), we can start by isolating \( c \).

First, let's add \( 17c \) to both sides:

\[
13c + 17c - 22 = 14
\]

This simplifies to:

\[
30c - 22 = 14
\]

Next, add \( 22 \) to both sides:

\[
30c = 14 + 22
\]

This simplifies to:

\[
30c = 36
\]

Now, divide both sides by \( 30 \):

\[
c = \frac{36}{30}
\]

Simplifying \( \frac{36}{30} \):

\[
c = \frac{6}{5}
\]

Thus, the value of \( c \) is

\[
\boxed{\frac{6}{5}}
\]

what is 6/5 simplified

The fraction \( \frac{6}{5} \) is already in its simplest form. The numerator (6) and the denominator (5) do not have any common factors other than 1.

Therefore, \( \frac{6}{5} \) cannot be simplified further. It can also be expressed as a mixed number:

\[
1 \frac{1}{5}
\]

But as a fraction, \( \frac{6}{5} \) is already simplified.