To solve the equation \( 9x - 6 = -8 \), we can first isolate \( x \) by rearranging the equation:
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Add 6 to both sides: \[ 9x = -8 + 6 \] \[ 9x = -2 \]
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Now, divide by 9: \[ x = -\frac{2}{9} \]
Next, we want to determine which of the given functions will result in solving the equation \( 9x - 6 = -8 \) in the form of \( f(x) = 0 \).
Rearranging the original equation gives us: \[ 9x - 6 + 8 = 0 \quad \text{or} \quad 9x + 2 = 0 \] This means we want to graph the function \( f(x) = 9x + 2 \) and find where it crosses the x-axis (i.e., where \( f(x) = 0 \)).
Looking at the options provided:
- A) \( f(x) = 17x - 6 \)
- B) \( f(x) = 9x - 14 \)
- C) \( f(x) = 9x + 2 \)
- D) \( f(x) = x - 6 \)
The correct function to graph for solving the equation is: C) \( f(x) = 9x + 2 \).