Question

Solve the equation.
StartFraction 3 x minus 19 Over 8 EndFraction equals StartFraction 5 x minus 6 Over 6 EndFraction
3x−19
8=
5x−6
6

Answer 1

To solve the equation

\[
\frac{3x - 19}{8} = \frac{5x - 6}{6},
\]

we can start by cross-multiplying to eliminate the fractions:

\[
6(3x - 19) = 8(5x - 6).
\]

Now, distribute both sides:

\[
18x - 114 = 40x - 48.
\]

Next, we can rearrange the equation to isolate \( x \). Start by moving all terms involving \( x \) to one side and constant terms to the other side:

\[
18x - 40x = -48 + 114.
\]

Simplifying both sides gives:

\[
-22x = 66.
\]

Now, divide both sides by -22:

\[
x = \frac{66}{-22} = -3.
\]

Thus, the solution to the equation is

\[
\boxed{-3}.
\]

To verify, substitute \( x = -3 \) back into the original equation:

Left side:

\[
\frac{3(-3) - 19}{8} = \frac{-9 - 19}{8} = \frac{-28}{8} = -\frac{7}{2}.
\]

Right side:

\[
\frac{5(-3) - 6}{6} = \frac{-15 - 6}{6} = \frac{-21}{6} = -\frac{7}{2}.
\]

Both sides are equal, confirming that \( x = -3 \) is correct.