**Find *x* if *f* ( *x* ) = 2 *x* + 7 and f( *x* ) = –1.**

**1 = *x***
**–4 = *x***
**0 = *x***
**–2 = *x***

We are given the function \( f(x) = 2x + 7 \) and the equation \( f(x) = -1 \).

To find \( x \), set \( f(x) = -1 \) and solve the equation:

\[
f(x) = 2x + 7
\]
\[
2x + 7 = -1
\]

Now solve for \( x \):

\[
2x = -1 - 7
\]
\[
2x = -8
\]
\[
x = \frac{-8}{2}
\]
\[
x = -4
\]

Thus, the solution is \( x = -4 \).

Would you like more details or explanations on any step?

Here are some related questions you might want to explore:
1. What happens if \( f(x) = 0 \)?
2. How do you solve similar equations with different coefficients?
3. How do you find \( f^{-1}(x) \) (the inverse function) in this case?
4. Can we use this function for solving inequalities?
5. What if the function involved squares, like \( f(x) = 2x^2 + 7 \)?

**Tip**: Always check your solution by plugging it back into the original equation.

Learn how to solve the linear equation f(x) = 2x + 7 when f(x) = -1 with a step-by-step breakdown. Understand key algebraic concepts and how to manipulate linear equations. Suitable for Grades 6-8.

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