Find the solution set of `(4-2x)/(3)gt(x)/(2)-3`.

Answer

To solve the inequality \(\frac{4-2x}{3} > \frac{x}{2} - 3\), we will follow these steps:

### Step 1: Rewrite the inequality
We start with the given inequality:
\[ \frac{4-2x}{3} > \frac{x}{2} - 3 \]

### Step 2: Eliminate the fractions
To eliminate the fractions, we can find a common denominator. The least common multiple of 3 and 2 is 6. We will multiply every term by 6:
\[ 6 \cdot \frac{4-2x}{3} > 6 \cdot \left(\frac{x}{2} - 3\right) \]

This simplifies to:
\[ 2(4 - 2x) > 3x - 18 \]

### Step 3: Distribute and simplify
Now we distribute on the left side:
\[ 8 - 4x > 3x - 18 \]

### Step 4: Move all terms involving \(x\) to one side
Next, we will add \(4x\) to both sides and add \(18\) to both sides:
\[ 8 + 18 > 3x + 4x \]
This simplifies to:
\[ 26 > 7x \]

### Step 5: Solve for \(x\)
Now, we divide both sides by 7:
\[ \frac{26}{7} > x \]
or equivalently,
\[ x < \frac{26}{7} \]

### Step 6: Write the solution set
The solution set can be expressed in interval notation as:
\[ x \in (-\infty, \frac{26}{7}) \]

### Final Answer
Thus, the solution set of the inequality \(\frac{4-2x}{3} > \frac{x}{2} - 3\) is:
\[ x \in (-\infty, \frac{26}{7}) \]

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