Questions: Solve the equation. First simplify the expression by combining like terms. 4/11 x + 4/3 = 3/2 - 7/11 x + 3/2

Solution Steps

To solve the given equation, we need to first simplify both sides by combining like terms. Then, we will isolate the variable \( x \) by moving all terms involving \( x \) to one side and constant terms to the other side. Finally, we will solve for \( x \).

We start with the equation:

\[ \frac{4}{11} x + \frac{4}{3} = \frac{3}{2} - \frac{7}{11} x + \frac{3}{2} \]

Combining the constant terms on the right side gives:

\[ \frac{4}{11} x + \frac{4}{3} = 3 - \frac{7}{11} x \]

Next, we move all terms involving \( x \) to one side and constant terms to the other side:

\[ \frac{4}{11} x + \frac{7}{11} x = 3 - \frac{4}{3} \]

This simplifies to:

\[ \frac{11}{11} x = 3 - \frac{4}{3} \]

Now, we simplify the right side:

\[ 3 - \frac{4}{3} = \frac{9}{3} - \frac{4}{3} = \frac{5}{3} \]

Thus, we have:

\[ x = \frac{5}{3} \]

Final Answer