Solve the following equations :
`(x-8)/(5)=(x-12)/(9)`

Options

A. `3`
B. `7`
C. `8`
D. `9`

Answer

To solve the equation \(\frac{x-8}{5} = \frac{x-12}{9}\), we will follow these steps:

### Step 1: Cross Multiply
We start with the equation:
\[ \frac{x-8}{5} = \frac{x-12}{9} \]
To eliminate the fractions, we cross-multiply:
\[ 9(x - 8) = 5(x - 12) \]

### Step 2: Distribute
Next, we distribute the numbers outside the parentheses:
\[ 9x - 72 = 5x - 60 \]

### Step 3: Move Terms Involving \(x\) to One Side
Now, we want all terms involving \(x\) on one side and constant terms on the other side. We can subtract \(5x\) from both sides:
\[ 9x - 5x - 72 = -60 \]
This simplifies to:
\[ 4x - 72 = -60 \]

### Step 4: Move Constant Terms to the Other Side
Next, we add \(72\) to both sides to isolate the term with \(x\):
\[ 4x = -60 + 72 \]
This simplifies to:
\[ 4x = 12 \]

### Step 5: Solve for \(x\)
Finally, we divide both sides by \(4\) to solve for \(x\):
\[ x = \frac{12}{4} \]
This gives us:
\[ x = 3 \]

### Final Answer
Thus, the solution to the equation is:
\[ \boxed{3} \]

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