Which value of x satisfies the equation start fraction, 4, divided by, 3, end fraction, left parenthesis, x, minus, start fraction, 3, divided by, 2, end fraction, right parenthesis, equals, start fraction, 22, divided by, 3, end fraction34​(*x*−23​)=322​?

To solve the equation 

\[
\frac{4}{3} \left(x - \frac{3}{2}\right) = \frac{22}{3},
\]

follow these steps:

1. **Distribute** \(\frac{4}{3}\) on the left side:

\[
\frac{4}{3} \cdot x - \frac{4}{3} \cdot \frac{3}{2} = \frac{22}{3}.
\]

This simplifies to:

\[
\frac{4}{3}x - \frac{12}{6} = \frac{22}{3}.
\]

Further simplifying \(\frac{12}{6}\):

\[
\frac{4}{3}x - 2 = \frac{22}{3}.
\]

2. **Add** \(2\) to both sides to isolate the term with \(x\). Since \(2\) can be written as \(\frac{6}{3}\):

\[
\frac{4}{3}x = \frac{22}{3} + \frac{6}{3}.
\]

3. **Combine** the fractions on the right side:

\[
\frac{4}{3}x = \frac{28}{3}.
\]

4. **Solve for \(x\)** by multiplying both sides by the reciprocal of \(\frac{4}{3}\), which is \(\frac{3}{4}\):

\[
x = \frac{3}{4} \cdot \frac{28}{3}.
\]

5. **Simplify** the expression:

\[
x = \frac{3 \cdot 28}{4 \cdot 3} = \frac{84}{12} = 7.
\]

So, the value of \(x\) that satisfies the equation is \(x = 7\).

Would you like further details or have any questions?

Here are five related questions:
1. What happens if the right-hand side of the equation was negative?
2. How would you solve this equation if the coefficients were different?
3. Can you explain why distributing fractions works in this equation?
4. What if the term inside the parentheses was more complex?
5. How do you check your solution for an equation involving fractions?

**Tip:** Always double-check your distribution step to ensure accuracy, especially when working with fractions.

Learn how to solve the equation (4/3)(x - 3/2) = 22/3 step-by-step with detailed explanations. This problem covers algebraic equations with fractions, suitable for students in Grades 7-9.

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