Question

Solve the equation. Choose the method you prefer to use. Check your answer.
StartFraction b Over 19 EndFraction
minusStartFraction 6 b Over 19 EndFraction
equalsStartFraction 10 Over 19 EndFraction

Answer 1

To solve the equation

\[
\frac{b}{19} - \frac{6b}{19} = \frac{10}{19},
\]

we can simplify the left-hand side. Since both fractions have the same denominator, we can combine them:

\[
\frac{b - 6b}{19} = \frac{10}{19}.
\]

This simplifies to:

\[
\frac{-5b}{19} = \frac{10}{19}.
\]

Next, we can eliminate the denominator by multiplying both sides of the equation by 19:

\[
-5b = 10.
\]

Now, to solve for \( b \), we divide both sides by -5:

\[
b = \frac{10}{-5} = -2.
\]

Now that we have found \( b = -2 \), let's check the solution by substituting \( b \) back into the original equation:

\[
\frac{-2}{19} - \frac{6(-2)}{19} = \frac{10}{19}.
\]

Calculating the left-hand side:

\[
\frac{-2}{19} + \frac{12}{19} = \frac{-2 + 12}{19} = \frac{10}{19}.
\]

Since the left-hand side equals the right-hand side, our solution checks out.

Thus, the final answer is

\[
\boxed{-2}.
\]