`(x-5)/2 - (x-3)/5 = 1/2`

Options

A. `7`
B. `9`
C. `8`
D. `7`

Answer

To solve the equation \((x-5)/2 - (x-3)/5 = 1/2\), we will follow these steps:

### Step 1: Find a common denominator
The denominators in the equation are 2 and 5. The least common multiple (LCM) of 2 and 5 is 10. We will multiply each term by 10 to eliminate the denominators.

\[ 10 \left( \frac{x-5}{2} \right) - 10 \left( \frac{x-3}{5} \right) = 10 \left( \frac{1}{2} \right) \]

### Step 2: Simplify each term
Now we simplify each term:

\[ 5(x-5) - 2(x-3) = 5 \]

### Step 3: Distribute the terms
Next, we distribute the terms inside the parentheses:

\[ 5x - 25 - 2x + 6 = 5 \]

### Step 4: Combine like terms
Now, we combine the like terms on the left side:

\[ (5x - 2x) + (-25 + 6) = 5 \]
\[ 3x - 19 = 5 \]

### Step 5: Isolate the variable
To isolate \(x\), we will add 19 to both sides of the equation:

\[ 3x - 19 + 19 = 5 + 19 \]
\[ 3x = 24 \]

### Step 6: Solve for \(x\)
Now, we divide both sides by 3 to solve for \(x\):

\[ x = \frac{24}{3} \]
\[ x = 8 \]

### Final Answer
The value of \(x\) is \(8\).

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