Solve for 'a' `(7)/(a-2)=(5)/(a+4)`

Options

A. `-19`
B. 38
C. 19
D. `-38`

Answer

To solve the equation \(\frac{7}{a-2} = \frac{5}{a+4}\), we can follow these steps:

### Step 1: Cross-Multiply
We start by cross-multiplying the fractions to eliminate the denominators:
\[ 7(a + 4) = 5(a - 2) \]

### Step 2: Distribute
Next, we distribute the numbers on both sides:
\[ 7a + 28 = 5a - 10 \]

### Step 3: Move Terms Involving 'a' to One Side
Now, we will move all terms involving \(a\) to one side and constant terms to the other side. We can subtract \(5a\) from both sides:
\[ 7a - 5a + 28 = -10 \]
This simplifies to:
\[ 2a + 28 = -10 \]

### Step 4: Move Constant Terms to the Other Side
Next, we subtract 28 from both sides:
\[ 2a = -10 - 28 \]
This simplifies to:
\[ 2a = -38 \]

### Step 5: Solve for 'a'
Finally, we divide both sides by 2 to solve for \(a\):
\[ a = \frac{-38}{2} = -19 \]

Thus, the solution for \(a\) is:
\[ \boxed{-19} \]