Question

What function should be graphed in order to solve the equation 9x - 6= -8 PLEASE can you explain step by step how you come up with the answer 9x+2 as the answer? How do you know and prove it? Thank you.
A)f(x)=17x-6
B)f(x)=9x-14
C)f(x)=9x+2
D)x-6

Answer 1

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.