To solve the equation \( 9x - 6 = -8 \), we first want to isolate \( x \). Here's how we can do it step by step:
Step 1: Add 6 to both sides
We start with: \[ 9x - 6 = -8 \] Adding 6 to both sides gives: \[ 9x - 6 + 6 = -8 + 6 \] This simplifies to: \[ 9x = -2 \]
Step 2: Divide by 9
Next, we divide both sides by 9: \[ x = \frac{-2}{9} \]
Finding the Corresponding Function
To find a function that corresponds to the original equation, we can rearrange the equation so that it is set to \( f(x) = 0 \).
The original equation rearranged is: \[ 9x - 6 + 8 = 0 \] This simplifies to: \[ 9x + 2 = 0 \] So, if we wanted to express this as a function, we can say: \[ f(x) = 9x + 2 \]
Match the Function to the Choices
From the choices given:
- A) \( f(x) = 17x - 6 \)
- B) \( f(x) = 9x - 14 \)
- C) \( f(x) = 9x + 2 \)
- D) \( f(x) = x - 6 \)
The correct choice is: C) \( f(x) = 9x + 2 \)
Verification
To verify that this function works for the equation \( 9x - 6 = -8 \), we can check if setting this function \( f(x) = 0 \) leads us back to the original equation.
If \( f(x) = 9x + 2 \), to find the \( x \) where \( f(x) = 0 \): \[ 9x + 2 = 0 \] Subtracting 2 from both sides: \[ 9x = -2 \] Dividing by 9: \[ x = \frac{-2}{9} \]
This is indeed the same \( x \) we found while solving the original equation. Therefore, the function \( f(x) = 9x + 2 \) is correct, confirming: C) \( f(x) = 9x + 2 \) as the answer.