Questions: Solve the equation. 4/6 x - 4 x + 8/3 = 4/3

Solution Steps

We start with the equation:

\[ \frac{4}{6} x - 4 x + \frac{8}{3} = \frac{4}{3} \]

To eliminate the fractions, we multiply every term by the least common denominator, which is 6:

\[ 6 \left(\frac{4}{6} x\right) - 6(4 x) + 6\left(\frac{8}{3}\right) = 6\left(\frac{4}{3}\right) \]

This simplifies to:

\[ 4x - 24x + 16 = 8 \]

Now, we combine like terms:

\[ -20x + 16 = 8 \]

Next, we isolate the variable \(x\) by subtracting 16 from both sides:

\[ -20x = 8 - 16 \]

This simplifies to:

\[ -20x = -8 \]

Now, we divide both sides by -20:

\[ x = \frac{-8}{-20} = \frac{8}{20} = \frac{2}{5} \]

Final Answer