Solve : `x/3-x/5=x/2-22`

Answer

To solve the equation \( \frac{x}{3} - \frac{x}{5} = \frac{x}{2} - 22 \), we can follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 3, 5, and 2. The least common multiple (LCM) of these numbers is 30.

### Step 2: Rewrite each term with the common denominator
We will express each term with a denominator of 30:
- \( \frac{x}{3} = \frac{10x}{30} \)
- \( \frac{x}{5} = \frac{6x}{30} \)
- \( \frac{x}{2} = \frac{15x}{30} \)

Now, we can rewrite the equation:
\[ \frac{10x}{30} - \frac{6x}{30} = \frac{15x}{30} - 22 \]

### Step 3: Simplify the left side
On the left side, we can combine the fractions:
\[ \frac{10x - 6x}{30} = \frac{4x}{30} \]

So, the equation now looks like:
\[ \frac{4x}{30} = \frac{15x}{30} - 22 \]

### Step 4: Eliminate the denominators
To eliminate the denominators, we can multiply the entire equation by 30:
\[ 4x = 15x - 660 \]

### Step 5: Rearrange the equation
Next, we will move all terms involving \( x \) to one side and constants to the other side:
\[ 4x - 15x = -660 \]
\[ -11x = -660 \]

### Step 6: Solve for \( x \)
Now, divide both sides by -11:
\[ x = \frac{-660}{-11} = 60 \]

### Final Answer
Thus, the solution to the equation is:
\[ x = 60 \]

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